0\lim\limits_{x->0^+} x \log(x)
1+\infty
2-\infty
30
41
5f(x)=\tan(x)
6\mathbb{R}
7(-\pi, \pi)
8f(x)
9f(x)
10f(x)
11f(x)
120
13\mathbb{R}
14f(x)
15\frac {e^n} {n!}
161
170
182x
19f(x)=|log(x)|
20\lim\limits_{ x\to+\infty} f(x)
210
221
23-\infty
24+\infty
25\lim\limits_{x\to+\infty} \frac{\exp(-x)}{\frac 1 x +2}
261
27-1
28-\infty
29+\infty
300
31f(x, y)=x^2+y^2
32x^2\leq1
33y
340
35f(x)=e^{-x^2} \cos(x)?
36x>0
37f(a)=f(-a)
38a<0
39f(a)=f(-a)
40\lim\limits_{x\to 0}
41f(x)=\frac{\sin x }{x}
420
431
44+\infty
45-\infty
46X
47Y
48\mathbb{E}(X)=\mathbb{E}(Y)=2
49\text{Var}(X)=3
50\text{Var}(Y)=1
51\text{Var}(X+Y)=4
52\text{Var}(X+Y)=5
53\text{Var}(X+Y)=8
54\text{Var}(X-Y)=2
55X
56Y
57\mathbb{E}(X)=\mathbb{E}(Y)=2
58\text{Var}(X)=3
59\text{Var}(Y)=1
60\text{Var}(X-Y)=4
61\text{Var}(X-Y)=2
62\text{Var}(X-2Y)=5
63\text{Var}(X-Y)=3
64X
65Y
66\mathbb{E}(X)=\mathbb{E}(Y)=3
67\text{Var}(Y)=3
68\text{Var}(X)=1
69\mathbb{E}(X+Y)=6
70\mathbb{E}(X-Y)=0
71\mathbb{E}(X+2Y)=9
72\text{Var}(X+Y)=\text{Var}(X-Y)=4
73X
74Y
75\mathbb{E}(XY)=\mathbb{E}(X)\cdot\mathbb{E}(Y)
76\mathbb{E}(X^2)=\mathbb{E}(X)^2
77\text{Var}(X)=\text{Var}(Y)
78X
79Y
80\text{Cov}(X, Y)=0
81Y
82\text{Var}(X)
83X
84Y
85\text{Var}(X)=1
86\text{Var}(Y)=2
87\text{Cov}(X, Y)=1
88\text{Var}(X+Y)=4
89\text{Var}(X+Y)=3
90\text{Var}(X+Y)=5
91\text{Var}(X+Y)=1
92X
93Y
94\text{Cov}(X, Y)=0
95\mathbb{E}(X, Y) \neq \mathbb{E}(X)\cdot \mathbb{E}(Y)
96\text{Var}(X)=\text{Var}(Y)
97\text{Var}(X)=2\text{Cov}(Y, X)
98X
99Y
100X
101Y
102X
103Y
104X
105Y
106X
107Y
108X
109Y
110\mathbb{E}(XY)=0
111\mathbb{E}(X)=\mathbb{E}(Y)=0
112\mathbb{E}(X)=0
113\mathbb{E}(Y)
114\mathbb{E}(Y)=0
115\mathbb{E}(X)
116\mathbb{E}(X)
117\mathbb{E}(Y)
118X
119X
120Y
121\text{Var}(X)=1
122\text{Var}(Y)=2
123\text{Cov}(X, Y)=0
124\text{Var}(X+Y)=4
125\text{Var}(X-2Y)=\text{Var}(X+2Y)=9
126\text{Var}(X-Y)=\text{Var}(X+Y)=1
127\text{Var}(X+2Y)=5
128X
129Y
130\text{Var}(X)=3
131\text{Var}(Y)=2
132\text{Cov}(X, Y)=1
133\text{Var}(X-2Y)=7
134\text{Var}(X+2Y)=7
135\text{Var}(X+Y)=5
136\text{Var}(X-Y)=6
137X
138\mathbb{E}(X)=2
139\mathbb{E}(X+2)=2
140\mathbb{E}(X-2)=0
141\mathbb{E}(X+1)=3
142\mathbb{E}(2X+4)=8
143X
144\text{Var}(X)=3
145\text{Var}(2X)=6
146\text{Var}(2X+3)=9
147\text{Var}(4X)=12
148\text{Var}(2X+3)=12
149X
150Y
151\text{Cov}(X, Y)=0
152\text{Var}(X)=\text{Var}(Y)
153X
154Y
155\mathbb{E}(X)=\mathbb{E}(Y)
156X
1574
1585
1593
160X
161Y
1623
1633
164X
165Y
1663
167X
168Y
1691
170X
171Y
172\text{Var}(X)=\text{Var}(Y)
173X=Y
174\mathbb{E}(X)=\mathbb{E}(Y)
175X=Y
176X
177Y
1781
179X
180\mu
181\sigma
182(X-\mu)
183\sigma
184\mu
1850<\mu<1
1861
187\mu
1881
1891
1900
191100
19210000
19310000
1940
195X
196X
197Y
198Y=3X+2
199\mathbb{E}(Y)=3 \mathbb{E}(X)
200\text{Var}(Y)=\text{Var}(X)
201\text{Var}(Y)=3 \text{Var}(X)
202\text{Var}(Y)=9 \text{Var}(X)+4
203\text{Var}(Y)=9 \text{Var}(X)
204Y
205X
206X
207Y
208X
209Y
210X
211Y
212X
213Y
214X
215Y
216\mathbb{E}(X)=\mathbb{E}(Y)=2
217\text{Cov}(X, Y)=3
218\text{Var}(Y)=4
219\text{Var}(X)=1
220X
221Y
222Y
223X
224Y=2+3X
225Y=-4+2X
226Y=-4+3X
227Y=3X
228Y=-4X+3
229Y=a+bX
230X
231Y
232X
233Y
234A=1
235B=1
236B=0
237A=0
238X
239Y
240\mathbb{R}^2
2411
242Dt=Ds+Dr
243Dt
244Ds
245Dr
2461
2470
2481
2491
250-1
2511
252-1
2531
2540
2551
256X
257Y
258X
259Y
260\text{Var}(X+Y)=\text{Var}(X)+\text{Var}(Y)-2\text{Cov}(X, Y)
261\text{Var}(X+Y)=\text{Var}(X)+\text{Var}(Y)+2\text{Cov}(X, Y)
262\mathbb{E}(X, Y)=\mathbb{E}(X)\cdot \mathbb{E}(Y)
263\text{Var}(X+Y)=\text{Var}(2X+Y)
264X
265Y
266\text{Cov}(X, Y)=\mathbb{E}(X)\cdot\mathbb{E}(Y)
267Y
268X
2690
270100
271100
27210000
273X
274\mathbb{E}(X)=0
275\text{Var}(X)=6
276 \mathbb{E}(X^2)
2775
2780
2793
2804
2816
282X
283\mathbb{E}(X)=0
284\text{Var}(X)=2
285 \mathbb{E}(X^2)
2862
2874
2888
2890
290X
291\mathbb{E}(X)=0
292\text{Var}(X)=16
293 \mathbb{E}(X^2)
2944
2950
2962
29716
298X
299\mathbb{E}(X)=0
300\text{Var}(X)=3
301 \mathbb{E}(X^2)
3023
3031
3042
3050
306X
307\mathbb{E}(X)=0
308\text{Var}(X)=1
309\mathbb{E}(X^2)
3102
3113
3121
3130
314X
315\mathbb{E}(X)=0
316\text{Var}(X)=0.5
317\mathbb{E}(X^2)
3181
3190.25
3200
3210.5
322X
323\mathbb{E}(X^2)\leq \mathbb{E}(X)
324X
3251
326X
327X
328\mathbb{E}(X^2)=4
329\mathbb{E}(X)=\sqrt{2}
330\text{Var}(X)
3312
3321
3330
3344
335X
336\mathbb{E}(X)=0
337\text{Var}(X)=7
338\mathbb{E}(X^2)
3393.5
3400
3410.7
342\sqrt{7}
3437
344X
345\mathbb{E}(X)=3
346\mathbb{E}(X^2)=10
347\text{Var}(X)
3482
3497
3501
35113
3520
353X
354\mathbb{E}(X)=3
355\mathbb{E}(X^2)=12
356\text{Var}(X)
3573
35815
35912
3602
361\mathbb{E}(X)=3
362\mathbb{E}(X^2)=9.5
363\text{Var}(X)
3643
3650
3660.5
3670.25
368X
369\mathbb{E}(X)=1
370\mathbb{E}(X^2)=2
371\text{Var}(X)
3723
3732
3741
3755
376X
377\mathbb{E}(X)=3
378\mathbb{E}(X^2)=10.5
379\text{Var}(X)
3801.5
3810.5
3822.5
3837.5
3840
385X
386\mathbb{E}(X)=2
387\mathbb{E}(X^2)=10
388\text{Var}(X)
3898
39098
39164
39212
3936
394X
395\mathbb{E}(X)=3
396\mathbb{E}(X^2)=20
397\text{Var}(X)
39811
39910
40023
40117
402391
403X
404\mathbb{E}(X)=2
405\mathbb{E}(X^2)=8
406\text{Var}(X)
4076
40810
4095
4104
411X
412\mathbb{E}(X)=3
413\mathbb{E}(X^2)=15
414\text{Var}(X)
4156
41612
41718
41836
419X
420\mathbb{E}(X)=5
421\mathbb{E}(X^2)=30
422\text{Var}(X)
42325
42430
42535
4265
427X
428\mathbb{E}(X)=1
429\mathbb{E}(X^2)=4
430\text{Var}(X)
4313
4322
4335
4340
435\mathbb{E}(XY)=-2
436\mathbb{E}(X)=-1
437\mathbb{E}(Y)=2
438X
439Y
440X
441Y
442X
443Y
444X
445Y
446X
447Y
448\mathbb{E}(X)=2
449\mathbb{E}(X)=1
450\mathbb{E}(XY)
4511
4522
4533
4544
455X
456Y
457\mathbb{E}(X)=6
458\mathbb{E}(Y)=2
459\mathbb{E}(XY)
4603
46112
4629
4638
464X
465Y
466\mathbb{E}(X)=3
467\mathbb{E}(Y)=1
468\mathbb{E}(XY)
4692
4701
4713
4720
473X
474Y
475\mathbb{E}(X)=5
476\mathbb{E}(Y)=1
477\mathbb{E}(XY)
4784
4796
4801
4810
4825
483X
484Y
485\mathbb{E}(X)=3
486\mathbb{E}(Y)=2
487\mathbb{E}(XY)
4881.5
4892
4906
4911
492X
493\mathbb{E}(X)=5
494\mathbb{E}(X^2)=4.5
495X
4960
4971
498X
4990
5001
501X
502X
503Y
504\text{Var}(X)=4
505\text{Var}(Y)=9
5060\leq\text{Cov}(X, Y)\leq6
507-6\leq\text{Cov}(X, Y)\leq6
508-36\leq\text{Cov}(X, Y)\leq36
5090\leq\text{Cov}(X, Y)\leq36
510X
511Y
512\text{Var}(X)=4
513\text{Var}(Y)=16
5140\leq\text{Cov}(X, Y)\leq64
515-64\leq\text{Cov}(X, Y)\leq64
5160\leq\text{Cov}(X, Y)\leq8
517-8\leq\text{Cov}(X, Y)\leq8
518X
519Y
520\text{Var}(X)=25
521\text{Var}(Y)=9
522|\text{Cov}(X, Y)|\leq25
523|\text{Cov}(X, Y)|\leq15
524|\text{Cov}(X, Y)|\leq225
525|\text{Cov}(X, Y)|\leq9
526X
527Y
528\text{Var}(X)=4
529\text{Var}(Y)=4
530\text{Cov}(X, Y)\leq4
531|\text{Cov}(X, Y)|\leq4
532-4\leq\text{Cov}(X, Y)\leq0
533|\text{Cov}(X, Y)|\leq 4
534-1
5353^{2x} + 3 \cdot 3^x - 4 \geq 0
536x
537x
538x
539x
540x
541p(x) = x^2 + 1
542x=i^2
543x=i^3
544x=i
545z=3 + 5i
5465i
547\mathbb{R}e(z)=i
548\mathbb{I}m(z) = 5
549z
550i=0
551z=0
552z=i
553z = a+bi
554w = c+di
555z + v = (a\ c) + (b\ d)i
556z \cdot v = (ac - bd) + (bc + ad)i
557z \cdot v = (a\ c) + (b\ d)i
558f \in C^2(\mathbb{R})
559\mathbb{R}
560f
561\mathbb{R}
562f^2
563\mathbb{R}
564f^2
565\mathbb{R}
566f^2
567\mathbb{R}
568f
569\mathbb{R}
570y = g(f(x))
571y
572g
573f
574y
575f
576g
577y = g(x)^{f(x)}
578y
579g
580f
581y = f(g(x))
582y
583g
584f
585y = g(x) \ f(x)
586f(x) = e^x + 1
587g(y) = y + 1
588f(g(y)) = e^{(y + 1)} + 2
589g(f(x)) = e^x + 1
590f(g(y)) = e^y + 1
591g(f(x)) = e^x + 2
592f(x) = \frac 1 x
593g(y) = \frac 1 y
594f(g(y)) = \frac{1}{1 + y}
595f(g(y)) = y + 1
596g(f(x)) = \frac{1}{1 + x}
597g(f(x)) = x + 1
598f(x) = e^x
599g(y) = \ln(y)
600f(g(y)) = y
601g(f(x)) = \ln(x)
602f(g(y)) = e^y
603g(f(y)) = \ln(e) = 1
604f(x)
605g(y)
606f(g(y))^{-1} = g^{-1}(f^{-1}(y))
607f
608g
609f
610g
611+\infty
612f(x)
613f(x) = \ln(x^2)
614f^{''}(x)
615 x^2
616\frac 2 x
617-\frac 2 x
618-\frac 1{x^2}
619-\frac 2{x^2}
620f(x) = e^x
621f^{''}(x)
622-e^x
623x
624-x
625e^x
6260
627f(x) = \ln(x) - x
628f^{'''}(x)
629\frac 2{x^3}
630\frac 1{x^3}
631- \frac1{x^2}
632\ln(x)
633-\frac 1{x^3}
634x^2+y^2=2
6351
6362
637\sqrt{2}
638\frac 1 2
639\mathbb{R}
640\lim\limits{x\to+\infty} = \lim\limits{ x \to -\infty} = +\infty
641f(x)
642f(x)
643f(x)
644f(x)
645X
646Y
647\text{Var}(X)=3
648\text{Var}(Y)=2
649\mathbb{E}(XY)=2
650\text{Var}(X+Y)
6515
6523
6531
654X
655Y
656\text{Var}(X)=2
657\text{Var}(Y)=3
658\text{Cov}(X, Y)=1
659\text{Var}(X+Y)
6606
6617
6624
663X
664Y
665\text{Var}(X)=2
666\text{Var}(Y)=4
667\text{Cov}(X, Y)=1
668\text{Var}(X+Y)
6698
6707
6716
6725
67310
674X
675Y
676\text{Var}(X)=2
677\text{Var}(Y)=4
678\text{Cov}(X, Y)=1
679\text{Var}(X+Y)
6807
6816
6828
6835
684X
685Y
686\text{Var}(X)=1
687\text{Var}(Y)=3
688\text{Cov}(X, Y)=1
689\text{Var}(X+Y)
6905
6916
6924
6932
694y = 3\sin(x) - 4\cos(x)
6953\cos((x) - 4\sin(x)
6963\sin(x) - 4\cos((x)
697-3\sin(x) - 4\cos((x)
698-3\cos((x) + 4\sin(x)
699-3\sin(x) + 4\cos((x)
7000
7011
7021
7031
704(0, 1)
705(0, 1)
706(0, e)
707(0, e)
708f(x) = \ln(x + 2)
709x \in (-2, +\infty)
710f(x)
711f(x)
712f(x)
713f(x)
714f(x)
715f(x) = e^x + 1
716x\in \left(-\infty , 0\right]
717f(x) = \tan(x)
718x\in \left(- \frac{\pi}{2}, \frac{\pi}{2}\right)
719X
720Y
721\text{Var}(X)=1
722\text{Var}(Y)=2
723\text{Cov}(X, Y)=1
724\text{Var}(2X-Y)
7251
7263
7272
7286
7294
730X
731Y
732\text{Var}(X)=1
733\text{Var}(Y)=2
734\text{Cov}(X, Y)=1
735\text{Var}(2X-3Y)
7364
73718
73810
73934
740X
741Y
742\text{Cov}(X, Y)=2
743X
744Y
7450.95
7460.5
747\mathbb{E}(X, Y)=\mathbb{E}(XY)
748\text{Var}(X)=\text{Var}(Y)
7490.75
7502000
75125\%
7522000
75325\%
7542000
75525\%
7562000
75725\%
7582000
7590.6
76051
76140\%
76251
76340\%
76451
76540\%
76651
76741
7686
7696
7706
7716
7726
773X
774X
775X
776X
777X
778\mathbb{E}(XY)=3
779\mathbb{E}(X)=1
780\mathbb{E}(Y)<3
781\mathbb{E}(Y)>3
782\mathbb{E}(Y)=3
783\mathbb{E}(Y)\leq3
784X
785\mathbb{E}(X)=3
786\mathbb{E}(X^2)=9
787\mathbb{E}(X-2)=1
788\mathbb{E}(X^2)=9
789X
790\mathbb{E}(X-3)=1
791\mathbb{E}(X^2)=\mathbb{E}(X)^2
792X
7930
7941
795X
796X
797X
7981
7991
800X
801100
802100
803100
8041
805\frac 1 k
806\frac k{k-1}
807\frac k{k-1}
808k
809f
810g
811A
812f(g(a))
813a
814A
815f(g(a))
816a
817A
818f(g(a))
819a
820A
821f(g(a))
822a
823A
8240
825X
826Y
827X
828Y
829x
830\tfrac{n+1}{2}Undefined control sequence \tfrac
831\tfrac n 2Undefined control sequence \tfrac
832\frac 1 4
833\frac 2 4
834\frac 3 4
8350.5
8364
83710
83810
83910
84010
84110
84210
8430.8
8443
84520\%
8463
84720\%
8483
84920\%
8503
8513
8520.95
8532
8545\%
8552
8565\%
8572
8585\%
8592
8602
8615\%
8625000
8635000
8645000
8650.05
8665000
8670.95
8685000
86920\%
8703
8710.8
8723
8730.2
8743
8750.6
8763
8770.5
8786
8796
880f(x) = x^4 + \cos(x)
88112x^2 + \sin(x)
88212x - \sin(x)
88324x - \sin(x)
88424x + \sin(x)
88524x^2 + \sin(x)
886f(x) \in \mathcal{C}^\infty
887f(x)
888f(x)
889f(x)
890f(x)
891f(x)
892f(x) = \cos(x)
8933
8941 - \frac{x^2}{2} - \frac{x^4}{24}
8951 + \frac{x^2}{2} + \frac{x^3}{6}
8961 - \frac{x^2}{2} + \frac{x^3}{6}
8971 + \frac{x^2}{2} - \frac{x^3}{6}
8981 - \frac{x^2}{2} + \frac{x^4}{24}
899f(x) = \sqrt{|x| - 2}
900 x \in (-\infty , -2) \cup (2, +\infty )
901 x > 2
902 x \in (-\infty , -2] \cup [2, +\infty )
903 x \in \mathbb{R}
904 x \in \mathbb{N}
905f(x) = \frac {1}{e^x - 17}
906x
907 x \neq e^{17}
908 x \neq \ln(e^{17})
909 x > \ln(17)
910 x \neq \ln(17)
911 x < \ln(17)
912f(x) = \sin\left(x - \sqrt{1 - 2x}\right)
913x
914 x \geq \frac{\pi}{2}
915 x \leq \frac{\pi}{2}
916 x \neq \frac{\pi}{2}
917 x = \frac{\pi}{2}
918 x \leq \frac{1}{2}
919f(x) = [\log(x)]^{\frac {1}{\log x}}
920x
921 x > 1
922 x \geq 1
923 x > 0 \wedge x \neq 1
924 x > 0
925 x \geq 0
926f(x) = x + \frac 1 x
927f(x) = 1 + \sin(x)
928f(x) = x - \frac 1 x
929\mathbb{R^+}
930\mathbb{R}
931\mathbb{R^-}
932\mathbb{R}
933\mathbb{R}
934f(x) =\frac 1 {1-x}
935g(x) = \sqrt{x -1}
936f \circ f(x) = \frac{x - 1}{x}
937g \circ g(x) = x^{\frac 1 2}
938g \circ f(x) = \frac{x}{x -1}^{\frac 1 2}
939f \circ g(x) = \frac{1}{1 - x^{1/2}}
940f \circ f(x) = \frac{1 - x}{x}
941f(x) = x - x^2
942g(y) = y^2 - y
943g(f(x))
944-x + 2x^2 - 2x^3 + x^4
945x^4 - 2x^3 - x
946x - 3x^2 - 4x 3 + x^4
947x + 2x^3 + x^4
948-x + 3x^2 - 4x^3 + 2x^4
949f(x) = \frac{3x}{2x+1}
950g(x) = \log(2x + 1)
951(g \circ f)(x)
952x = 1
953\log3
954\frac {2\log3 + 1}{3\log3}
955\frac{3\log3}{2\log3 + 1}
9563\log3
9570
958f(x) = e^{2x}
959x = 0
9602
961e
9621
963+\infty
964-\infty
965f(x) = \frac{x+1}{x-2}
966\frac{3}{(x - 2)^2}
967-\frac{3}{(x - 2)^2}
968\frac{x + 3}{(x - 2)^2}
969\frac{x - 3}{(x - 2)^2}
970\frac {1}{(x - 2)^2}
971f(x) = \ln(98x)
972\frac 1{x^2}
973\frac{98}{x^2}
974\frac{1}{98x^2}
975-\frac{98}{x^2}
976-\frac{1}{x^2}
977f(x) = x\sin(x)
978\cos(x) + x\sin(x)
979x\cos(x) + \cos(x)
980\sin(x) + \cos(x)
981x\cos(x) + \sin(x)
982x\sin(x) + \sin(x)
983f(x) = x^{\frac 5 3}
984\frac{5}{9} \ x^{\frac 5 3}
985\frac{10}{9} \ x^{-\frac 1 3}
986\frac{10}{9} \ x^{\frac 1 3}
987\frac{10}{3} \ x^{-\frac 1 3}
988\frac{10}{3} \ x^{\frac 1 3}
989y = \sin^2(x) + \cos^2(x)
990x
991y = 1
992y = -1
993y = 2
994y = 0
995y = e
996f(x) = \frac {\cos(x)}{\sin(x)}
997\frac 1 {\sin^2(x)}
998-\frac 1 {\sin(x)}
999-\frac 1 {\sin^2(x)}
1000\frac 1 {\sin(x)}
1001 \frac {-1}{- sin(x)}
1002f(x) = e^{x\ \ln(x)}
1003f^{'}(x) = e^{x\ \ln(x)}
1004f^{'}(x) = e^{\ln x + 1}
1005f^{'}(x) = e^{x\ \ln(x)} \ [x\ \ln(x)]
1006f^{'}(x) = e^{x\ \ln(x)} \ [\ln x + 1]
1007f^{'}(x) = e^0 = 1
1008f(x) = x^2 \ \ln x + 3x
10092x\ \ln x + x
10102x \ \ln x + 3
1011\ln x + x + 3
1012\ \ln(2x) + x + 3
10132x \ \ln x + x + 3
1014f(x) = 0
1015f^{'}(x)
1016f^{'}(x) = -\infty
1017f^{'}(x) = 0
1018f^{'}(x) = +\infty
1019X
1020100
1021100
1022100
1023f(x) = x^3
1024x\geq 0
1025log_a(x)
1026a>1
1027x>0
1028x \to 0
1029+\infty
1030x \to -\infty
10310
1032x \to +\infty
1033+\infty
1034f: A \subseteq \mathbb{R} \to \mathbb{R}
1035x_0 \in A
1036f
1037f
1038x_0
1039f
1040f
1041f
1042F(x_0+h)-f(x_0) = hf^{'}(x0) + o(h)
1043D[f(x) + g(x)] = f^{'}(x) + g^{'}(x)
1044D[f(x)g(x)] = f^{'}(x)g(x) + f(x)g^{'}(x)
1045D[f(x)/g(x)] = \frac{f^{'}(x)g(x) - f(x)g^{'}(x)}{g(x)}
1046D[f(g(x))] = f^{'}(g(x))g^{'}(x)
1047f(x) = \sin(x)
1048[0: 2\pi]
1049\pi \leq x < 2\pi
10500 \leq x \leq \frac \pi 2 e \frac {3\pi}2 \leq x < 2\pi
1051Ax=b
1052 \Leftrightarrow \det A \neq 0
1053 \Leftrightarrow r(A) = r(A|b)
1054 \Leftrightarrow\ r(A) = r(A+b)
1055 \Leftrightarrow\ r(A) \leq r(A|b)
1056f(x) = x^4 + 1
1057x
1058y
1059f(x) = a^x
1060a>1
1061x\to -\infty
1062\mathbb{R}
1063f(x) = a^x
1064a<1
1065x\to +\infty
1066\mathbb{R}
1067A
1068k
1069f: A \subseteq \mathbb{R} \to \mathbb{R}
1070\forall \ x1, x2 \in A
1071x1 < x2
1072f(x1)
1073\forall \ x1, x2 \in A
1074x1 < x2
1075f(x1)\leq f(x2)
1076\forall \ x1, x2 \in A
1077x1 < x2
1078f(x1)>f(x2)
1079\forall \ x1, x2 \in A
1080x1 < x2
1081f(x1)\geq f(x2)
1082f: A \subseteq \mathbb{R} \to \mathbb{R}
1083 \forall \ x1, x2 \in A
1084x1 < x2
1085f(x1)
1086\forall \ x1, x2 \in A
1087x1 < x2
1088f(x1)\leq f(x2)
1089\forall \ x1, x2 \in A
1090x1 < x2
1091f(x1)>f(x2)
1092\forall \ x1, x2 \in A
1093x1 < x2
1094f(x1)\geq f(x2)
1095f(x) = f(-x)\,\forall \ x \in \mathbb{R}
1096y
1097\mathbb{N},\mathbb{Z},\mathbb{Q}
1098\mathbb{Z},\mathbb{Q},\mathbb{R}
1099\mathbb{Q},\mathbb{N},\mathbb{R}
1100\mathbb{R},\mathbb{N},\mathbb{Z}
1101\mathbb{N},\mathbb{Z},\mathbb{Q},\mathbb{R}
1102\mathbb{N}
1103\mathbb{Z}
1104\mathbb{Q}
1105\mathbb{R}
1106\mathbb{C}
1107\mathbb{R}
1108\mathbb{Q}
11092^{10}+2^{10}
11102^{20}
11114^{10}
11122^{11}
11134^{20}
11142^{100}
1115{\left(3^n-3^{n+1}+3^{n+2}\right)}^2
11167^2\cdot 9^n
11173^{2n+2}
11182\cdot 3^{n+1}
11199^{2n+2}
11207\cdot 3^n
1121{\left(\frac{1}{2}\right)}^{10}
1122\left(\frac{1}{4}\right)^{10}
1123\left(\frac{1}{2}\right)^5
1124\left(\frac{1}{4}\right)^9
1125\left(\frac{1}{2}\right)^9
1126\left(\frac{1}{2}\right)^{11}
1127x=\sqrt{5+\sqrt{2}}
1128y=\sqrt{2+\sqrt{5}}
1129\frac{1}{x}>\frac{1}{y}
1130x^2
1131xy<0
1132\frac{1}{y}<-\frac{1}{x}
1133x^2>y^2
11340
1135{\left(\frac{2}{x}\right)}^{-2}
1136-\frac{2}{x}
1137\frac{4}{x^2}
1138-\frac{x^2}{4}
1139\frac{x^2}{4}
11404x^2
1141\sqrt[4]{x^3}
1142x^{\frac{4}{3}}
1143x^{\frac{3}{4}}
1144x^{\frac{2}{\sqrt{3}}}
1145x^{\frac{3}{2}}
1146x^{\frac{4}{\sqrt{3}}}
11473^{x-1}-1
1148{\left(\frac{1}{3}\right)}^x-1
1149{\left(\frac{1}{3}\right)}^{x-1}
1150\frac{1}{3}\left(3^x+3\right)
1151\frac{1}{3}{\left(\frac{1}{3}\right)}^{-x}-1
1152\frac{1}{3}\left(3^x-1\right)
1153-\frac{1}{\sqrt[2]{x^3}}
1154x^{\frac{3}{2}}
1155x^{-\frac{2}{3}}
1156-x^{\frac{2}{3}}
1157-x^{\frac{3}{2}}
1158-x^{-\frac{3}{2}}
1159{\left(a+b\right)}^2-{\left(a-b\right)}^2
11600
11612{\left(a+b\right)}^2
11621
1163a^2+b^2
11644ab
1165{\left(m+n\right)}^2-\left(m+n\right)\left(m-n\right)
1166n\left(m-n\right)
11672n\left(m+n\right)
1168m+n
1169m^2-n^2
1170n\left(m+n\right)\left(m-n\right)
1171\frac{2x-x^2+4y-2xy}{2-x}
11724y-2xy
11732-x
1174x+2y
1175x+4y-2xy
1176\left(x+1\right)\left(x-1\right)\left(x^2+1\right)\left(x^4+1\right)+1
1177x^8+1
1178x^4
1179x^{16}+2
1180x^8
1181x^8+5
1182\frac{12x^2+5x-2}{4x-1}
11833x-5
11843x+2
1185x-\frac{3}{4}
11863x
11874-x
1188P\left(x\right)
1189x^2-9
11903
1191-3
1192P\left(x\right)
1193\sqrt{3}
1194-\sqrt{3}
1195P\left(x\right)
11963
1197P\left(x\right)
11989
1199P\left(x\right)
1200-\sqrt{3}
1201P\left(x\right)
1202\sqrt{x^2}
1203x
1204-x
1205\pm x
1206\left|x\right|
1207\sqrt{\left|x\right|}
1208\sqrt{4{\left(x-3\right)}^2}
1209x<3
12104x-12
121112-4x
12122x-6
12136-2x
1214\frac{x-1}{4-x^2}\le 0
1215x\ge 1
1216x>2
1217-22
1218x\le -2\vee x\ge 1
1219x<-2\vee 1\le x<2
1220n
1221n
1222\mathbb{R}
1223n!
1224\mathbb{C}
1225\mathbb{R}
1226n
1227\mathbb{R}
1228n
1229\mathbb{C}
1230k
1231x^2-kx+k+1=0
1232x
1233k=\pm 1
1234k=0
1235k=1
1236k=-1
1237k
1238\left(9x^2-16\right)\left(x^3-8\right)=0
12392
12403
12415
1242x
1243y
1244x>y
1245xy>0
1246\frac{1}{x}>\frac{1}{y}
1247\frac{1}{x}<\frac{1}{y}
1248x^2>y^2
1249x>0\wedge y>0
1250x>0\vee y>0
1251x
1252x\left|x\right|>0
1253\frac{x}{\left|x\right|}>0
1254x+\left|x\right|>0
1255x-\left|x\right|<0
1256-x\left|x\right|<0
1257x
1258\left|-x\right|\left|x\right|
1259x
1260-x
1261\left|x\right|
1262x^2
1263-x^2
1264\sqrt{4}
12654
1266-2
1267\pm \sqrt{2}
1268\pm 2
12692
1270\left|x-4\right|=3
1271x^2+x+1=0
1272ax^2+bx+c=0
1273\mathbb{R}
1274\mathbb{R}
1275\mathbb{R}
1276\mathbb{C}
1277\mathbb{C}
1278\left|x-1\right|=\left|x+2\right|
1279ax+by=0
1280ax+b=0
1281ax^2+by+c=0
1282ax+by+c=0
1283ax^2+by^2+c=0
1284y=mx+q
1285q=0
1286y=mx+q
1287m<0
1288P\left(x_0,y_0\right)
1289P
1290y=mx+x_0
1291y+y_0=m\left(x+x_0\right)
1292y=m\left(x-x_0\right)
1293y-y_0=m\left(x-x_0\right)
1294y=mx_0+y_0
1295k
1296y=\left(k^2-1\right)x-k
1297k<-1\vee k>1
1298k=0
1299-1\le x\le 1
1300k=\pm 1
1301\ \forall k\in \mathbb{R}
1302A\left(x_A,y_A\right)
1303B\left(x_B,y_B\right)
1304\sqrt{{\left(x_A-y_A\right)}^2+{\left(y_B-y_B\right)}^2}
1305\sqrt{{\left(x_A+y_A\right)}^2-{\left(y_B+y_B\right)}^2}
1306\sqrt{{\left(x_A-x_B\right)}^2+{\left(y_A-y_B\right)}^2}
1307\sqrt{{\left(x_A+x_B\right)}^2-{\left(y_A+y_B\right)}^2}
1308\sqrt{{\left(x_A-x_B\right)}^2-{\left(y_A-y_B\right)}^2}
1309\left(k^2-1\right)x+2ky-1=0
1310k
1311P
1312Q
1313m
1314m
1315P
1316k
1317m
1318Q
1319k
1320P
1321Q
1322k
1323m
1324P
1325Q
1326k
1327m
1328k
1329y=ax^2+bx+c
1330k
1331y=-\left(k-2\right)x^2+2kx-k^3
1332k=2
1333k<2
1334k\ge 2
1335k\le 2
1336k>2
1337k
1338y=\left(k-2\right)x^2-2\left(k-1\right)x+k
1339k=2
1340k=1
1341k=0
1342k=-1
1343k
13444x^2+4y^2=1
1345x^2+y^2=4x
13462
1347\left(0,-2\right)
13484
1349\left(2,0\right)
13502
1351\left(2,1\right)
13524
1353\left(-2,0\right)
13542
1355\left(2,0\right)
1356\frac{x^2}{a^2}+\frac{y^2}{b^2}=-1
1357\frac{x}{a^2}+\frac{y}{b^2}=-1
1358\frac{x^2}{a^2}+\frac{y^2}{b^2}=1
1359\frac{x}{a^2}-\frac{y}{b^2}=1
1360\frac{x^2}{a^2}-\frac{y^2}{b^2}=1
13619x^2+4y^2=36
13629
13634
13643
13652
1366\frac{9}{2}
13672
13684
13699
13702
13713
1372e=1
1373x>0
1374x\ge 0
1375y\ge 0
1376y\neq 0
1377{\mathbb{R}}^2
1378\frac{x^2}{4}-y^2=1
1379y=\pm 2x
1380y=\pm 4x
1381y=\pm \frac{1}{2}x
1382y=\pm \frac{1}{4}x
1383y=\pm x
1384y=\frac{ax+b}{cx+d}
1385x=\frac{b}{a}
1386y=-\frac{c}{a}
1387x=-\frac{d}{c}
1388y=\frac{a}{d}
1389x=-\frac{a}{d}
1390y=\frac{b}{a}
1391x=-\frac{c}{a}
1392y=-\frac{d}{c}
1393x=\frac{a}{c}
1394y=\frac{b}{d}
1395A\left(0,0\right)
1396B\left(4,0\right)
1397C\left(2,2\right)
1398D\left(0,2\right)
13991
14002
14013
14026
140312
1404y=3x-4
1405y=x^2-2x+2
1406\left(2,2\right)
1407\left(3,5\right)
1408\left(-2,2\right)
1409\left(-5,3\right)
1410\left(-2,-2\right)
1411\left(3,5\right)
1412\left(2,-2\right)
1413\left(5,-3\right)
1414\left(2,2\right)
1415\left(-3,5\right)
1416x=2
1417F\left(4,2\right)
1418F
1419x=4
1420x=0
1421y=0
1422y=2
1423y=mx
1424f\left(x\right)
1425T
1426f\left(x\right)=f\left(T\right)
1427f\left(x\right)=f\left(x\right)+T
1428f\left(x\right)=\frac{f\left(x\right)}{T}
1429f\left(x\right)=f\left(x+T\right)
1430f\left(x\right)=Tf\left(x\right)
1431y=A{\sin \left(Bx+C\right)}
1432C
1433B
1434A
1435B
1436C
1437A
1438A
1439B
1440C
1441A
1442C
1443B
1444C
1445A
1446B
1447y={\sin x}
1448x=0
1449x=k\pi
1450x=2k\pi
1451x=\frac{\pi}{2} + k \pi
1452x=\frac{\pi}{2} + 2k \pi
1453f\left(x\right)={\sin x}
1454g\left(x\right)={\cos x}
1455g
1456\pi
1457f
1458f
1459\frac{\pi }{4}
1460g
1461g
1462\frac{\pi }{2}
1463f
1464f
1465\pi
1466g
1467g
1468\frac{\pi }{2}
1469f
1470y={\tan x}
1471\mathbb{R}
1472x\neq k\pi
1473x\neq 2k\pi
1474x\neq \frac{\pi}{2}+k\pi
1475x\neq \frac{\pi}{4}+2k\pi
1476y={\tan x}
1477y={\cos x}
1478\cos \alpha =x
1479\cos \left(\frac{\pi}{2}-\alpha \right)=x
1480\sin \left(\frac{\pi}{2}-\alpha \right)=x
1481{\cos \left(2\pi -\alpha \right)}=-x
1482\cos \left(\frac{\pi}{2}+\alpha \right)=x
1483\sin \alpha =x
1484{\cos \left(2x\right)}
14852{{\cos}^{2} x}-1
14861-2{{\sin}^{2} x}
1487{{\cos}^{2} x}-{{\sin}^{2} x}
1488y=\sqrt{3}{\cos x}-{\sin x}
1489y=\sqrt{3}{\cos \left(x+\frac{\pi}{3}\right)}
1490y=2{\cos \left(x+\frac{\pi}{6}\right)}
1491y=2{\sin \left(x+\frac{\pi}{6}\right)}
1492y=\sqrt{3}{\cos \left(x-\frac{\pi}{3}\right)}
1493y=2{\cos \left(x-\frac{\pi}{6}\right)}
1494f:A\to B
1495\ \forall x_1,x_2\in Ax_1\neq x_2\Longrightarrow f\left(x_1\right)\neq f\left(x_2\right)
1496\ \forall x_1,x_2\in Ax_1\neq x_2\Longrightarrow f\left(x_1\right)=f\left(x_2\right)
1497\ \forall x_1,x_2\in Ax_1\neq x_2\Longrightarrow f\left(x_1\right)\ge f\left(x_2\right)
1498\ \forall x_1,x_2\in Ax_1\neq x_2\Longrightarrow f\left(x_1\right)\le f\left(x_2\right)
1499f:X\to Y
1500y\in Y
1501x\in X
1502y\in Y
1503x\in X
1504y\in Y
1505x\in X
1506x\in X
1507y\in Y
1508x\in X
1509y\in Y
1510f:X\to \mathbb{R}
1511X
1512X
1513f\left(X\right)\subseteq \mathbb{R}
1514f\left(X\right)\subseteq \mathbb{R}
1515f\left(X\right)\subseteq \mathbb{R}
1516f:X\to \mathbb{R}
1517X
1518X
1519f\left(X\right)\subseteq \mathbb{R}
1520f\left(X\right)\subseteq \mathbb{R}
1521f:X\to \mathbb{R}
1522f
1523f
1524f
1525f
1526f:X\to Y
1527x\in X
1528y\in Y
1529x\in X
1530y\in Y
1531y\in Y
1532x\in X
1533y\in Y
1534x\in X
1535y\in Y
1536x\in X
1537f\left(x\right)={\sin x}
1538g\left(x\right)={\cos x}
1539x\in \left[0,2\pi \right]
1540f\left(x\right)=e^x
1541g\left(x\right)=-{\arctan x}
1542\mathbb{R}
1543f\left(x\right)>g\left(x\right)\ \forall x\in \mathbb{R}
1544f\left(x\right)\le g\left(x\right)\ \forall x\in \mathbb{R}
1545y
1546f\left(x\right)=e^x
1547g\left(x\right)={\cos x}
1548f\left(x\right)\ge g\left(x\right)\ \forall x
1549f\left(x\right)\le g\left(x\right)\ \forall x
1550f\left(x\right)>g\left(x\right)\ \forall x\ge 0
1551f\left(x\right)\ge g\left(x\right)\ \forall x\ge 0
1552f
1553f\left(a\right)<0
1554f\left(b\right)>0
1555\left(a,b\right)
1556\left(a,b\right)
1557\left(a,b\right)
1558\left(a,b\right)
1559f\left(x\right)
1560g\left(x\right)
1561h\left(x\right)=f\left(g\left(x\right)\right)
1562f
1563g
1564g
1565f
1566f
1567g
1568g
1569f
1570f
1571g
1572f:\mathbb{R}\to \mathbb{R}
1573x>0
1574x>k
1575k\in \mathbb{R}
1576f:\mathbb{R}\to \mathbb{R}
1577xf\left(x\right)=0
1578x=1
1579x=f\left(x\right)
1580x=0
1581x=\frac{1}{f\left(x\right)}
1582x=-\frac{1}{f\left(x\right)}
1583-\frac{2}{f\left(x\right)}\le 0
1584x
1585f\left(x\right)=0
1586f\left(x\right)\neq 0
1587f\left(x\right)>0
1588f\left(x\right)<0
1589\exists x\in \mathbb{R}
1590y={{log}_{\frac{1}{2}} x}
1591\left(0,+\infty \right)
1592\left[0,+\infty \right)
1593\left(0,+\infty \right)
1594\left[0,+\infty \right)
1595\mathbb{R}
1596y=\frac{1}{x}
1597\left(-\infty, 0\right)\cup \left(0, +\infty \right)
1598\mathbb{R}
1599\left(-\infty , 0\right)\cup \left(0, +\infty \right)
1600\left(0,+\infty \right)
1601\mathbb{R}
1602y=e^{-x}
1603\mathbb{R}
1604y<0
1605x>0
1606\mathbb{R}
1607\mathbb{R}
1608y>0
1609x>0
1610y>0
1611x\ge 0
1612y\le 0
1613y=\frac{1}{x}
1614\mathbb{R}
1615\mathbb{R}
1616x>0
1617\mathbb{R}
1618\mathbb{R}
1619y>0
1620x\neq 0
1621y\neq 0
1622x>0
1623y>0
1624y=\frac{x+1}{\sqrt{x^2-1}}
1625x\le -1\vee x\ge 1
1626x\neq 1
1627-1
1628x<-1\vee x>1
1629x\ge 1
1630y=\frac{\left|x\right|}{x}\frac{1}{\left|x-2\right|}
1631x\neq 0
1632x\neq 0
1633x\neq 2
1634x>0
1635x<0\vee x>2
1636x\neq \pm \sqrt{2}
1637y=x^2
1638\mathbb{R}
1639x>0
1640-2
1641x>-2
1642x\le 2
1643y=x^2
1644-2
1645\mathbb{R}
1646-1\le x\le 1
1647\mathbb{R}
1648y=x^2
1649x<0
1650y=\frac{1}{x^2}
1651y=\sqrt{x}
1652y=-\frac{1}{x^2}
1653y=\sqrt{-x}
1654y={{log}_{\frac{1}{2}} x}
1655y={\left(\frac{1}{2}\right)}^{-x}
1656y=2^x
1657y=\frac{1}{{{log}_{\frac{1}{2}} x}}
1658y={log}_2x
1659y=2^{-x}
1660{\ln \left(x+1\right)}+{\ln \left(x-1\right)}=1
1661x=1
1662x=\sqrt{e}
1663x=\sqrt{e-1}
1664x=\sqrt{e+1}
1665y=\frac{1}{\sqrt{e}+1}
1666\frac{2^{2x}}{2}-4\cdot 2^{x-1}-16=0
1667x=2
1668x=3
1669x=3
1670x=4
1671x=2
1672x=-4
1673x=8
1674y=x\left(2x-1\right)
1675y=\frac{x^2}{x-1}
1676y=e^x
1677y={\ln \left(x^2\right)}
1678y={{\ln}^{2} x}
1679y=x^2+1
1680y=x-1
1681y=\left|{\ln x}\right|
1682y={\arctan x^2}
1683y={\arctan x}
1684y=x
1685y=x
1686y=-x
1687y=x^2
1688y=\sqrt{x}
1689y={\sin x}
1690y={\cos x}
1691y=e^x
1692y={\ln x}
1693y=e^x
1694y=e^{-x}
1695\mathbb{R}
1696{\arctan x}
1697y={\left(\frac{1}{e}\right)}^x
1698y={{\sin}^{2} x}
1699y={\arctan \left(x^2\right)}
1700y=\frac{1}{\left(1+x^2\right)}
17012{\cos x}-1\le 0
17020
17032\pi
1704\frac{\pi }{6}\le x\le \frac{11}{6}\pi
1705\frac{\pi }{3}\le x\le \frac{5}{3}\pi
1706\frac{\pi }{4}\le x\le \frac{7}{4}\pi
1707\frac{\pi }{2}\le x\le \frac{3}{2}\pi
17080\le x\le \pi
1709{\cos x}\left({\sin x}-1\right)\ge 0
17100
17112\pi
1712\frac{\pi }{6}\le x\le \frac{11}{6}\pi
1713\frac{\pi }{3}\le x\le \frac{5}{3}\pi
1714\frac{\pi }{4}\le x\le \frac{7}{4}\pi
1715\frac{\pi }{2}\le x\le \frac{3}{2}\pi
17160\le x\le \pi
1717{\left({\cos x}-1\right)}^2={{\cos}^{2} x}
1718x=\pm \frac{\pi }{6}+2k\pi
1719x=\pm \frac{\pi }{3}+k\pi
1720x=\pm \frac{\pi }{4}+k\pi
1721x=\pm \frac{\pi }{6}+k\pi
1722x=\pm \frac{\pi }{3}+2k\pi
1723e^x={\ln x}
1724e^{-x}={\left(\frac{1}{e}\right)}^x
1725{\ln x^2}=2{\ln x}
1726{\ln x}=4-x^2
1727{\arctan x}=2-e^x
1728{\tan x}={\cos x}
17290
17301
17312
17323
1733y=\frac{1}{1+x^2}
1734y>0
1735y\ge 1
17360\le x<1
17370\le x\le 1
17380
1739y={\sin x}{\cos x}
17402\pi
1741\pi
1742\frac{\pi}{2}
17432
1744\frac{1}{2}
1745y=\left|{\sin x}{\cos x}\right|
17462\pi
1747\pi
1748\frac{\pi}{2}
17492
1750\frac{1}{2}
1751{\lim_{x\to x_0} f\left(x\right)}
1752x_0
1753f\left(x\right)
1754f\left(x\right)
1755x_0
1756x_0
1757f\left(x\right)
1758f\left(x\right)
1759x_0
1760f\left(x\right)
1761x_0
1762x_0
1763A
1764x_0
1765A
1766x_0
1767A
1768x_0
1769A
1770x_0
1771A
1772x_0
1773A
1774{\lim_{x\to x_0} f\left(x\right)}
1775x\to x^+_0
1776x\to x^-_0
1777x\to x^+_0
1778x\to x^-_0
1779x\to x^+_0
1780x\to x^-_0
1781x\to x^+_0
1782x\to x^-_0
1783f\left(x_0\right)
1784\lim_{x\to - \infty } f\left(x\right) = +\infty
1785f\left(x\right)
1786f\left(x\right)
1787f\left(x\right)
1788f\left(x\right)
1789f\left(x\right)
1790f\left(x\right)
1791x\neq x_0
1792{\lim_{x\to x_0} f\left(x\right)}
1793{\lim_{x\to x_0} f\left(x\right)}
1794{\lim_{x\to x_0} f\left(x\right)}
1795{\lim_{x\to x_0} f\left(x\right)}=0
1796{\lim_{x\to x_0} f\left(x\right)}=x_0
1797f\left(x\right)
1798x=x_0
1799{\lim_{x\to x_0} f\left(x\right)}=0
1800{\lim_{x\to x_0} f\left(x\right)}=x_0
1801{\lim_{x\to x_0} f\left(x\right)}=f\left(x_0\right)
1802{\lim_{x\to x_0} f\left(x\right)}=\infty
1803{\lim_{x\to x_0} f\left(x\right)}
1804{\lim_{x\to x^-_0} f\left(x\right)}=y_1
1805{\lim_{x\to x^+_0} f\left(x\right)}=y_2
1806y_1,y_2\in \mathbb{R}
1807f\left(x\right)
1808x_0
1809f\left(x\right)
1810x_0
1811f\left(x\right)
1812x_0
1813x=x_0
1814f\left(x\right)
1815y=y_1
1816y=y_2
1817f\left(x\right)
1818{\lim_{x\to x_0} f\left(x\right)}=y_0\neq f\left(x_0\right)
1819f\left(x\right)
1820x_0
1821f\left(x\right)
1822x_0
1823f\left(x\right)
1824x_0
1825x=x_0
1826f\left(x\right)
1827y=y_1
1828y=y_2
1829f\left(x\right)
1830f\left(x\right)
1831{\lim_{x\to 2} f\left(x\right)}=+\infty
1832\mathbb{R}
1833-2\le x\le 2
18342
1835\left[-a,a\right]
1836a\in \mathbb{R}
1837\left[2-a,2+a\right]
1838a\ge 2
1839{\lim_{x\to -\infty } \frac{x+{\sin x}}{x-{\cos x}}}
1840+\infty
1841-\infty
18421
1843\pi
1844\lim_{x\to +\infty } \frac{\sqrt{x}-\sqrt[5]{x}}{\sqrt{x}+\sqrt5{x}}
18450
18461
18475
1848\infty
1849{\lim_{x\to 0} \frac{e^{{\sin x}}-{{\cos}^{2} x}}{x}}
1850-1
18511
1852-e
1853e
1854{\lim_{x\to 0} \frac{x}{1-{\cos x}}}
18550
18561
1857\frac{1}{2}
1858-\frac{1}{2}
1859\infty
1860{\lim_{x\to 1} \frac{{\sin \left(\pi x\right)}}{\exp{x}-e}}
1861\pi e
1862-\frac{e}{\pi }
1863\frac{\pi }{e}
1864-\frac{\pi }{e}
1865\frac{\pi }{e}
1866{\lim_{x\to 0^+} x^x}
1867+\infty
1868-\infty
18690
18701
1871e
1872{\lim_{x\to +\infty } {\left(x+e\right)}^{\frac{1}{{\ln x}}}}
18730
18741
1875e
1876+\infty
1877-\infty
1878{\lim_{x\to 0} \frac{{\sin x}-x^2}{{\ln \left(x+1\right)}}}
18790
18801
1881e
1882+\infty
1883-\infty
1884{\lim_{x\to e^+} \frac{{\sin \left(\frac{\pi }{e}x\right)}}{{\ln \left(x-e\right)}}}
18850
18861
1887e
1888\frac{e}{\pi }
1889\frac{\pi }{e}
1890{\lim_{x\to 0} {\sin \left(\frac{1}{x}\right)}}
18910
18921
1893\pi
1894\infty
1895f:\mathbb{R}\to \mathbb{R}
1896y=1
1897y=2x
1898{\lim_{x\to -\infty } \frac{f\left(x\right)}{x}}=2
1899{\lim_{x\to +\infty } f\left(x\right)}=x
1900{\lim_{x\to -\infty } f\left(x\right)}=2x
1901{\lim_{x\to +\infty } f\left(x\right)}=1
1902{\lim_{x\to -\infty } f\left(x\right)}=1
1903{\lim_{x\to +\infty } f\left(x\right)}=2
1904{\lim_{x\to -\infty } f\left(x\right)}=1
1905{\lim_{x\to +\infty } \frac{f\left(x\right)}{x}}=2
1906{\lim_{x\to -\infty } \frac{f\left(x\right)}{x}}=2
1907{\lim_{x\to +\infty } f\left(x\right)}=1
1908f\left(x\right)=\frac{x^3-3x^2-x+3}{x-3}
1909x=3
1910f\left(3\right)=0
1911f\left(3\right)=3
1912f\left(3\right)=4
1913f\left(3\right)=8
1914f\left(3\right)=9
1915f:\left(a,b\right)\to \mathbb{R}
1916f
1917x
1918{\lim_{h\to 0} \frac{f\left(x+h\right)-f\left(x\right)}{a-b}}
1919{\lim_{x\to h} \frac{f\left(x+h\right)-f\left(x\right)}{a-b}}
1920{\lim_{h\to 0} \frac{f\left(x+h\right)-f\left(x\right)}{h}}
1921{\lim_{x\to h} \frac{f\left(x+h\right)-f\left(x\right)}{b-a}}
1922{\lim_{x\to h} \frac{f\left(x+h\right)-f\left(x\right)}{h}}
1923f
1924x_0
1925x_0
1926x_0
1927x_0
1928x_0
1929x_0
1930f
1931x_0
1932f
1933x_0
1934f
1935x_0
1936f
1937x_0
1938f^{''}
1939x_0
1940f^{''}
1941x_0
1942f:\left(a,b\right)\to \mathbb{R}
1943x_0\in \left(a,b\right)
1944f
1945x_0
1946f^{'}\left(x_0\right)=0
1947f^{'}\left(x_0\right)=0
1948f
1949x_0
1950f
1951x_0
1952f\left(x_0\right)=0
1953f\left(x_0\right)=0
1954f
1955x_0
1956f
1957x_0
1958x_0
1959f
1960x_0
1961f
1962x_0
1963f
1964x_0
1965f
1966x_0
1967f
1968f
1969f^{'}\left(x_0\right)=0
1970f^{''}\left(x_0\right)<0
1971x_0
1972f
1973x_0
1974f
1975x_0
1976f
1977x_0
1978f
1979x_0
1980f
1981f
1982x_0
1983x_0
1984x_0
1985x_0
1986x_0
1987x_0
1988x\to 0
1989f^{'}\left(x\right)
1990m
1991n
1992m\neq n
1993x_0
1994f
1995x_0
1996f
1997x_0
1998f^{'}
1999x_0
2000f
2001x_0
2002f^{'}
2003x\to x_0
2004f^{'}\left(x\right)
2005-\infty
2006+\infty
2007x_0
2008f
2009x_0
2010f
2011x_0
2012f^{'}
2013x_0
2014f
2015x_0
2016f^{'}
2017f:\left[a,b\right]\to \mathbb{R}
2018\left[a,b\right]
2019\left(a,b\right)
2020c\in \left[a,b\right]:\frac{f\left(b\right)-f\left(a\right)}{b-a}=f^{'}\left(c\right)
2021c\in \left[a,b\right]:\frac{f\left(b\right)-f\left(a\right)}{b-a}=f\left(c\right)
2022c\in \left[a,b\right]:\frac{f\left(b\right)-f\left(a\right)}{b+a}=f\left(c\right)
2023c\in \left(a,b\right):\frac{f\left(b\right)-f\left(a\right)}{b-a}=f^{'}\left(c\right)
2024c\in \left(a,b\right):\frac{f\left(b\right)-f\left(a\right)}{b+a}=f\left(c\right)
2025f\left(x\right)=e^{2x}+{\ln \left(3x\right)}
20263e^{3x}+\frac{1}{x}
20273x+\frac{1}{2x}
20282e^{2x}+\frac{1}{x}
20292e^{2x}+\frac{1}{3x}
2030e^{2x}+\frac{1}{x}
2031f\left(x\right)=\sqrt{{\sin \left(2x\right)}}
2032\frac{{\cos \left(2x\right)}}{\sqrt{{\sin \left(2x\right)}}}
2033\frac{{\sin \left(2x\right)}}{2\sqrt{{\cos \left(2x\right)}}}
2034\frac{{\cos \left(2x\right)}}{\sqrt{{\cos \left(2x\right)}}}
2035\frac{{\cos \left(2x\right)}}{2\sqrt{{\sin \left(2x\right)}}}
2036\frac{{\sin \left(2x\right)}}{\sqrt{{\cos \left(2x\right)}}}
2037f\left(x\right)=2^{x^2}
20382 x 2^{x^2}
2039x^2 2^{x^2}
20402 x 2^{x^2}\ln 2
2041x^2 2^{x^2}\ln 2
20422 x^2 2^{x^2}\ln 2
2043f\left(x\right)=\sqrt{x-2}
2044\mathbb{R}
2045x\neq 2
2046x\ge 0
2047x>2
2048x\ge 2
2049f\left(x\right)=e^{x^2}
2050f\left(x\right)={\left(x-1\right)}^{50}
2051f^{\left(n\right)}\left(x\right)
2052n-
2053n
2054f^{\left(n\right)}\left(x\right)\equiv 0
2055n=0
2056n=1
2057n=49
2058n=50
2059n=51
2060f\left(x\right)
2061f\left(x\right)\equiv f^{'}\left(x\right)
2062f\left(x\right)={\ln x}
2063f\left(x\right)=1
2064f\left(x\right)=e^x
2065f\left(x\right)=x
2066f\left(x\right)=\sqrt{x}
2067f\left(x\right)
2068f\left(x\right)=kf^{'}\left(x\right)
2069k
2070f\left(x\right)={\ln x}
2071f\left(x\right)=1
2072f\left(x\right)=e^{2x}
2073f\left(x\right)=2x
2074f\left(x\right)=\sqrt{x}
2075k
2076f\left(x\right)=x^2-5x+6
2077g\left(x\right)=kx-3k-4
2078\left(1,2\right)
2079k=-1
2080k=2
2081k=-3
2082k=4
2083k=-5
2084k
2085f\left(x\right)=\frac{x^2-1}{x-k}
2086x
20871
2088k=0
2089k=1
2090k=\pm 1
2091k
2092k
2093n=4k+2
2094k\in \mathbb{N}
2095f^{\left(n\right)}\left(x\right)
2096n-
2097f\left(x\right)={\sin x}
2098f^{\left(n\right)}\left(x\right)=f\left(x\right)
2099f^{\left(n\right)}\left(x\right)=-f\left(x\right)
2100f^{\left(n\right)}\left(x\right)=f^{'}\left(x\right)
2101f^{\left(n\right)}\left(x\right)=-f^{'}\left(x\right)
2102f^{\left(n\right)}\left(x\right)=k!f\left(x\right)
2103n-
2104f\left(x\right)=x^n
2105n\in \mathbb{N}
2106f^{\left(n\right)}\left(x\right)=n!x
2107f^{\left(n\right)}\left(x\right)=n!
2108f^{\left(n\right)}\left(x\right)=n^n
2109f^{\left(n\right)}\left(x\right)=n
2110f^{\left(n\right)}\left(x\right)=0
2111k
2112f\left(x\right)=\frac{k\left(x-1\right)}{x^2-4}
2113k=0
2114k=1
2115k=2
2116k
2117k
2118f\left(x\right)=x-{\ln \left(x^2-1\right)}
2119x=0
2120x=1+\sqrt{2}
2121x=1+\sqrt{2}
2122x=1+\sqrt{2}
2123x=1-\sqrt{2}
2124x=1+\sqrt{2}
2125x=1-\sqrt{2}
2126f\left(x\right)=ax^2+bx+c
2127a,b,c\in \mathbb{R}
2128a\neq 0
2129a>0
2130b,c\neq 0
2131f\left(x\right)=\left|x\right|
2132f^{'}\left(x\right)
2133f^{'}(0) = 2
2134f^{'}
2135f^{'}
2136x=0
2137f^{'}
2138\mathbb{R}
2139f^{'}
2140x=0
2141f^{'}\left(x\right)
2142f\left(x\right)=\sqrt[3]{x}
2143\mathbb{R}
2144x=0
2145\mathbb{R}
2146x=0
2147\left[-\infty ,0\right)
2148y=e^{x+2}
2149x=-1
2150x=0
2151x=e
2152x=e^{-1}
2153x\in \mathbb{R}
2154f:\mathbb{R}\to \mathbb{R}
2155f
2156y=l
2157l\in \mathbb{R}
2158x\to +\infty
2159{\lim_{x\to +\infty } f\left(x\right)}=+\infty
2160{\lim_{x\to l} f^{'}\left(x\right)}=+\infty
2161{\lim_{x\to +\infty } f\left(x\right)}=0
2162{\lim_{x\to l} f^{'}\left(x\right)}=l
2163{\lim_{x\to +\infty } f^{'}\left(x\right)}=0
2164f:\mathbb{R}\to \mathbb{R}
2165I\subset \mathbb{R}
2166f^{'}\left(x\right)\equiv 0\ \forall x\in \mathbb{R}
2167f\left(x\right)\equiv k\ \forall x\in \mathbb{R}
2168k\in \mathbb{R}
2169f^{'}\left(x\right)\equiv k\ \forall x\in I
2170k\in \mathbb{R}
2171f\left(x\right)\equiv 0\ \forall x\in I
2172f^{'}\left(x\right)\equiv k\ \forall x\in \mathbb{R}
2173k\in \mathbb{R}
2174y=P_3\left(x\right)
2175P_3\left(x\right)
2176\mathbb{R}
2177\mathbb{R}
2178\mathbb{R}
2179\mathbb{R}
2180\mathbb{R}
2181f\in C^{\infty }\left(\mathbb{R}\right)
2182\left(1,0\right)
2183f\left(1\right)=0
2184f\left(1\right)=f^{'}\left(1\right)=0
2185f^{''}\left(1\right) > 0
2186f^{'}\left(1\right)=0
2187f\left(1\right)=f^{'}\left(1\right)=0
2188f^{''}\left(1\right) < 0
2189f^{''}\left(1\right)=0
2190y=e^{{\sin \left(x\right)}}
2191x=k\pi
2192k\in \mathbb{Z}
2193x=\pi +2k\pi
2194k\in \mathbb{Z}
2195x=\frac{3}{2} \pi+2k\pi
2196k\in \mathbb{Z}
2197x=\frac{\pi }{2}+2k\pi
2198k\in \mathbb{Z}
2199x=\frac{\pi }{4}+2k\pi
2200k\in \mathbb{Z}
2201y=e^{{\cos \left(2x\right)}}
2202y=\pi
2203x=k\pi
2204k\in \mathbb{Z}
2205y=e
2206x=e+2k\pi
2207k\in \mathbb{Z}
2208y=\frac{1}{e}
2209y={\cos \left({\ln x}\right)}
2210f
2211g
2212\left(x_0,y_0\right)
2213f\left(x_0\right)=g\left(x_0\right)=y_0
2214f^{'}\left(x_0\right)=g^{'}\left(x_0\right)
2215f\left(x_0\right)=f^{'}\left(x_0\right)\wedge g\left(x_0\right)=g^{'}\left(x_0\right)
2216f\left(x_0\right)=g\left(x_0\right)\vee f^{'}\left(x_0\right)=g^{'}\left(x_0\right)
2217f\left(x_0\right)=g\left(x_0\right)=y_0\wedge f^{'}\left(x_0\right)=g^{'}\left(x_0\right)
2218I=\left[-3,0\right]
2219y=\frac{x^3-5x+2}{x+3}
2220I
2221f\left(x\right)={\cos \left(e^x\right)}
2222x_n
2223n\in \mathbb{R}
2224f\left(x\right)
2225{\lim_{n\to \infty } \left|x_{n+1}-x_n\right|}=e
2226{\lim_{n\to \infty } \left|x_n\right|}=0
2227{\lim_{n\to \infty } \left|x_{n+1}-x_n\right|}=0
2228{\lim_{n\to \infty } \left|x_n\right|}=e
2229{\lim_{n\to \infty } \left|x_{n+1}-x_n\right|}=+\infty
2230y=\sqrt{{\sin \left(x\right)}+x}
2231x=\pi +2k\pi
2232k\in \mathbb{N}
2233x=\pi +k\pi
2234k\in \mathbb{N}
2235x=\pi +2k\pi
2236k\in \mathbb{N}
2237x=\pi +2k\pi
2238k\in \mathbb{N}
2239x=\pi +2k\pi
2240k\in \mathbb{N}
2241f\left(x\right)=\sqrt{{\sin \left(x\right)}+x}
2242g\left(x\right)={\cos x}
2243g\left(x\right)=\sqrt{{\sin \left(x\right)}+x}
2244g\left(x\right)=\sqrt{x}
2245g\left(x\right)=\sqrt{{\sin \left(x\right)}}
2246g\left(x\right)=x
2247f,g\in C^{\infty }\left(\mathbb{R}\right)
2248f^{'}\left(x\right)\equiv g^{'}\left(x\right)
2249f\left(x\right)\equiv g\left(x\right)+k
2250k\in \mathbb{R}
2251f^{''}\left(x\right)\equiv g^{''}\left(x\right)
2252f^{'}\left(x_0\right)g^{'}\left(x_0\right)\ge 0\ \forall x_0\in \mathbb{R}
2253f:\left[a,b\right]\to \mathbb{R}
2254f:\left[a,b\right]\to \mathbb{R}
2255f
2256g
2257f\le g
2258\int{f}>\int{g}
2259\int{f}\ge \int{g}
2260\int{f}<\int{g}
2261\int{f}\le \int{g}
2262\int{f}=\int{g}
2263\int{f}=\int{\left|f\right|}
2264\int{\left|f\right|}\le \int{f}
2265\left|\int{f}\right|\le \int{\left|f\right|}
2266\left|\int{f}\right|\ge \int{f}
2267\left|\int{f}\right|=\int{\left|f\right|}
2268f\left(x\right)
2269\left[a,b\right]
2270t\in \left[a,b\right]
2271\int^b_a{f\left(x\right)dx}=t\left(b-a\right)
2272\int^b_a{f\left(x\right)dx}=t\left(a-b\right)
2273\int^b_a{f\left(x\right)dx}=f\left(t\right)\left(b-a\right)
2274\int^b_a{f\left(x\right)dx}=f\left(t\right)\frac{1}{a-b}
2275\int^b_a{f\left(x\right)dx}=t\left(b-a\right)
2276k
2277f\left(x\right)
2278\left[-k,k\right]
22790
2280f\left(x\right)=0
2281xf\left(x\right)=0
2282f\left(0\right)=0
2283f\left(x\right)
2284f\left(x\right)
2285f\left(x\right)
2286f\left(x\right)
2287\int{f\left(x\right)dx}=f\left(x\right)+k
2288k
2289f\left(x\right)={\ln x}
2290f\left(x\right)=x
2291f\left(x\right)=e^x
2292f\left(x\right)=1
2293f\left(x\right)=\frac{1}{e^x}
2294f\left(x\right)={{\sin}^{2} x}
2295\int{f\left(x\right)dx}
2296x{\sin x} + k
2297\frac{1}{2}\left(x-{\cos x}\right)+ k
2298x{\sin x}{\cos x} + k
2299\frac{1}{2}\left(x-{\sin x}{\cos x}\right) + k
2300\frac{1}{2}\left(x+{\sin x}\right) + k
2301f\left(x\right)=e^x-2^x
2302\int{f\left(x\right)dx}
2303e^x+\frac{2^x}{{\ln 2}}+k
2304\frac{1}{x}+2^x{\ln 2}+k
2305e^x-2^x+k
2306\frac{1}{x}-2^x+k
2307e^x-\frac{2^x}{{\ln 2}}+k
2308f\left(x\right)={\sin \left(2x\right)}+2{\cos \left(x\right)}
2309\int{f\left(x\right)dx}
2310\frac{{\cos \left(2x\right)}}{2}-2{\sin \left(x\right)}+k
23112{\sin \left(x\right)}-\frac{{\cos \left(x\right)}}{2}+k
2312\frac{{\sin \left(x\right)}}{2}+{\cos \left(2x\right)}+k
23132{\sin \left(x\right)}-\frac{{\cos \left(2x\right)}}{2}+k
23142{\sin \left(x\right)}-2{\cos \left(2x\right)}+k
2315f\left(x\right)=xe^{x+1}
2316\int{f\left(x\right)dx}
2317xe^{x+1}+k
2318x^2e^{x+1}+k
2319\left(x+1\right)e^{x+1}
2320\left(x-1\right)e^{x+1}+k
2321\left(x+x+1\right)e^{x+1}+k
2322f\left(x\right)=x{\sin x}{\cos x}
2323\int{f\left(x\right)dx}
2324\frac{1}{4}\left(2{\sin x}-x{\cos x}\right)+k
2325\frac{1}{8}\left({\sin \left(2x\right)}-2{\cos \left(2x\right)}\right)+k
2326\frac{1}{2}\left(2x{\sin \left(x\right)}+{\cos \left(x\right)}\right)+k
2327\frac{1}{8}\left({\sin \left(2x\right)}-2x{\cos \left(2x\right)}\right)+k
2328\frac{1}{8}\left(2x{\sin \left(2x\right)}+{\cos \left(2x\right)}\right)+k
2329f\left(x\right)=\frac{x+1}{x^2-5x+6}
2330\int{f\left(x\right)dx}
23314{\ln \left|x-3\right|}-3{\ln \left|x-2\right|}+k
23324{\ln \left|x-2\right|}+3{\ln \left|x-3\right|}+k
23335{\ln \left|x-3\right|}-4{\ln \left|x-2\right|}+k
23344{\ln \left|x+3\right|}+5{\ln \left|x-2\right|}+k
23356{\ln \left|x-3\right|}-3{\ln \left|x+2\right|}+k
2336f\left(x\right)=\frac{2}{x^2-2x+1}
2337\int{f\left(x\right)dx}
23382{\tan \left(x-1\right)+k}
2339\frac{2}{x-1}+k
2340{\arctan \left(x+1\right)+k}
2341-\frac{2}{x-1}+k
23424{\tan {\left(x-1\right)}^2}+k
2343f\left(x\right)=\frac{3}{x^2+9}
2344F\left(x\right)={\tan \left(\frac{x}{3}\right)}-1
2345F\left(x\right)=\frac{3}{x+3}+2
2346F\left(x\right)={\arctan \left(x\right)}-3
2347F\left(x\right)=\frac{{\left(x-3\right)}^2}{3}+5
2348F\left(x\right)={\arctan \left(\frac{x}{3}\right)}-7
2349f\left(x\right)=\frac{1}{x+x{\ln \left(x\right)}}
2350F\left(x\right)=x{\ln x}+e
2351F\left(x\right)={\ln \left({\ln x}\right)}+\pi
2352F\left(x\right)=\frac{1}{{\ln \left({\ln x}\right)}}+e
2353F\left(x\right)={\ln \left({\ln x}+1\right)+\pi }
2354F\left(x\right)={\arctan \left(\frac{x}{{\ln x}+1}\right)+e}
2355f\left(x\right)=x{\sin \left(x\right)}
2356\left[0,\pi \right]
23570
23581
2359\pi
2360\frac{\pi }{2}
23612\pi
2362\int^{e^2}_e{\frac{1}{x{\ln x}}}dx
2363e
2364\frac{1}{e^2}
2365{\ln e}
2366\frac{1}{{\ln 2}}
2367{\ln 2}
2368f\left(x\right)={\sin x}e^{{\cos x}}
2369\left[-\pi ,\pi \right]
23700
2371\frac{1}{2}
2372e^{\pi }
2373\frac{e^{\pi }}{2\pi }
2374y=\left|x\right|
2375x
2376x=\pm 2
23770
23781
23792
23804
23818
2382\int^{\frac{\pi }{4}}_{-\frac{\pi }{4}}{\frac{x^2{\tan \left(x\right)}\left(1+x^4\right)}{\left|x\right|}}dx
23830
23841
23852\pi
2386+\infty
2387-\infty
2388\int^{\pi }_0{\frac{1+{\cos x}}{\sqrt{x+{\sin x}}}dx}
23892\pi
23901
23912\sqrt{\pi }
23921-\sqrt{\pi }
2393\frac{1}{\sqrt{\pi }}
2394\int^{+\infty }_{-\infty }{\frac{1}{9+x^2}dx}
2395{\pi }^2
23969\pi
23973\pi
2398\frac{\pi }{3}
23993{\pi }^2
2400\int^{+\infty }_{-\infty }{{\tan x}dx}
24010
24021
2403\pi
2404{\pi }^2
2405\int^{+\infty }_{-\infty }{e^{-x^2}dx}
2406\sqrt{\pi}
24071
2408e
2409e^2
2410\int^{+\infty }_{-\infty }{{\sin x}dx}
24110
24121
2413\pi
2414\infty
2415a = b^x
2416x
2417a
2418a
2419b
2420x
2421a
2422b
2423a
2424x
2425y
2426y = \ln(|x| -1)
2427-1 < x < 1
2428x > 1
2429x < 1
24302^{15}
24312^{16}
24322^{30}
24334^{15}
24344^{16}
24354^{30}
2436\cos(2x) = \sin^2(x) - \cos^2(x)
2437\tan(x) = \frac{\sin(x)}{\cos(x)}
2438\sin(45^{\circ}) = \frac 1 2
2439\sin^2(x) = 1 + \cos^2(x)
2440\sin(2x) = \cos^2(x) - \sin^2(x)
2441\log(20^2)
24422 \ (1+\log2)
24432 + \log{20}
24442 \ \log4 \ \log5
24452 \ \log2
24462 + \log2
2447\log(10 x^2) = 4
2448x
244940
245010^2
24512
245225
24534^{10}
245412'000
24555\%
2456150
2457300
245860
2459600
246015
2461y = ax^2 + bx + c
2462b^2 - c > 0
2463a > 0
2464b^2 - 4ac < 0
2465b < 0
2466a - b = 2c
2467V=(-2 , 4)
2468 y = -x^2 - 4x
2469 y = x^2 - 4x
2470 y = -x^2 + 4x
2471 y = x^2 + 4x
2472 y = -x^2 -4
24731
2474b
24751
2476ab
2477a
2478b
2479a
2480b
2481a
2482b
2483a
2484b
2485x - 2y + 1 = 0
24862x + y = 0
24872y - x = 0
24882x - y = 0
2489x - 2y = 0
2490x + 2y = 0
2491 \frac{1}{x^2}
2492x^2
2493\sin x
2494\tan x
2495\sqrt x
2496f(x) = \ln(x-2)^2
2497g(x) = 2\ln(x-2)
2498f(x) = x^2 + 2
2499g(x) = \sin(x)
2500f(g(x))
2501\sin(x^2 + 2)
2502\sin^2(x + 2)
2503\sin(x^2) + 2
2504\sin^2(x)
2505\sin^2(x) + 2
2506c
2507f(x) + g(x)
2508c
2509f
2510g
2511c
2512c
2513f
2514g
2515c
2516f
2517g
2518f(x) = \sin x \cos x
2519\sin(2x)
2520\cos(2x)
2521-\sin(2x)
2522-\cos(2x)
2523f(x) = \sin x \cos x
2524\sin(3x)
2525\cos(3x)
2526-\sin(3x)
2527-\cos(3x)
2528c
2529c
2530c
2531f(x) = \cos(x^2)
2532g(x) = (\cos x)^2
25332\pi
2534k
2535f(x) = k|x|
2536x = 0
2537k
2538 k = 0
2539 k < 0
2540 k > 0
2541k
2542U
2543f^{'}(c) = 0
2544c \in U
2545c
2546c
2547c
2548c
2549f(x) = \sin x
2550g(x) = \tan x
2551x
2552\frac \pi 2
2553f(x) = \arctan x + \arctan \frac 1 x
2554f(x) = 2x^3 - 3x^2
2555\mathbb{R}
2556f(x) = 2x - 1
2557g(x) = 2x + 1
2558g(x) = {x - 1}2
2559g(x) = 1{2x - 1}
2560g(x) = 1{2x + 1}
2561g(x) = \frac{x + 1}{2}
2562a, b>0
2563\sqrt a + \sqrt b = \sqrt{a +b}
2564\sqrt a \sqrt b = \sqrt a b
2565\sqrt {a^2} = a
2566\sqrt {a^3} = a \sqrt a
2567\sqrt{3-|2+x|}
2568x
2569- 2 \leq x \leq + 2
2570– 5 \leq x \leq + 3
2571\forall x
2572x \neq 2
2573– 5 \leq x \leq + 1
2574y=2x+3
2575y=9-x
2576{\sin \theta }{\cos \theta }
2577{\sin \theta }{\cos \theta }
2578{{\sin}^{2} \theta }
2579{{\cos}^{2} \theta }
2580{{\sin}^{2} \theta }+{{\cos}^{2} \theta }
2581{{\sin}^{2} \theta }-{{\cos}^{2} \theta }
2582v=3+2i
2583w=2-5i
2584vw=5-3i
2585vw=5-10i
2586vw=6-11i
2587vw=16-11i
2588vw=16-10i
2589v=2-i
25902
2591i
25922
2593-1
25942
25950
25962
2597-1i
2598-1
25992
2600z
2601z=\frac{3+i}{2-3i}
2602\frac{5}{3}+\frac{4}{3}i
2603\frac{5}{3}-\frac{4}{3}i
2604\frac{3}{13}+\frac{11}{13}i
2605\frac{3}{13}-\frac{11}{13}i
2606\frac{3}{13}-\frac{11}{13}i
26071
26082
26094
26100
2611y=\left|x\right|
2612x=\left|y\right|
2613-\left|x\right|\le y\le \left|x\right|
2614-\left|x\right|
2615-\left|y\right|\le x\le \left|y\right|
2616-\left|y\right|
2617\rho
2618\theta
2619k-
2620k\rho
2621k\theta
2622k\rho
2623\theta
2624{\rho }^k
2625k\theta
2626{\rho }^k
2627\theta
2628{\rho }^k
2629\frac{\theta }{k}
2630\rho
2631\theta
2632-
2633\sqrt[n]{\rho }
2634\frac{\theta }{n}+2k\pi
26350\le k\le n
2636\sqrt[n]{\rho }
2637\theta +\frac{2k\pi }{n}
26380
2639\sqrt[n]{\rho }
2640\frac{\theta }{n}+\frac{2k\pi }{n}
26410\le k\le n-1
2642\sqrt[n]{\rho }
2643\frac{\theta }{n}+\frac{2k\pi }{n}
26440
2645\sqrt[n]{\rho }
2646\frac{\theta }{n}+\frac{2k\pi }{n}
26470\le k\le n^2
2648f:A\to B
2649\ \forall x_1,x_2\in Ax_1\neq x_2\Longrightarrow f\left(x_1\right)\neq f\left(x_2\right)
2650\ \forall x_1,x_2\in Ax_1\neq x_2\Longrightarrow f\left(x_1\right)=f\left(x_2\right)
2651\ \forall x_1,x_2\in Ax_1\neq x_2\Longrightarrow f\left(x_1\right)\ge f\left(x_2\right)
2652\ \forall x_1,x_2\in Ax_1\neq x_2\Longrightarrow f\left(x_1\right)\le f\left(x_2\right)
2653f:R\to R
2654\left[a,b\right]
2655\ \forall x_1,x_2\in \left[a,b\right]x_1f\left(x_2\right)
2656\ \forall x_1,x_2\in \left[a,b\right]x_1
2657\ \forall x_1,x_2\in \left[a,b\right]x_1
2658\ \forall x_1,x_2\in \left[a,b\right]x_1
2659\ \forall x_1,x_2\in \left[a,b\right]x_1
2660f
2661\left[a,b\right]
2662f
2663f\left(x\right)={\sin x}
2664g\left(x\right)=\sqrt{2-x^2}
2665h\left(x\right)={\ln x}
2666k\left(x\right)={\ln \sqrt{{{\cos}^{2} x}+1}}
2667k\left(x\right)=f\left(g\left(h\left(x\right)\right)\right)
2668k\left(x\right)=h\left(g\left(f\left(x\right)\right)\right)
2669k\left(x\right)=g\left(h\left(f\left(x\right)\right)\right)
2670k\left(x\right)=f\left(h\left(g\left(x\right)\right)\right)
2671k\left(x\right)=h\left(f\left(g\left(x\right)\right)\right)
2672f\left(x\right)={\ln \frac{xe^x}{3+x^2}}
2673x\to \infty
2674{\lim_{x\to 0} {\left(\frac{x{\ln \left(1+x\right)}}{1-{\cos x}}\right)}^{3-x}}
2675{\lim_{x\to 0^+} \left[{\ln x}-{\ln {\arcsin \left(7x\right)}}\right]}
26767
2677\frac{1}{7}
2678{\ln 7}
2679{\ln \frac{1}{7}}
26801
2681{\lim_{x\to 0} \frac{\left[{\ln \left(1+4x\right)}-4{\sin \left(x+x^2\right)}\right]}{x}}
26820
26831
2684-1
26853
2686{\lim_{x\to 0} \frac{{{\tan \left(5x\right)}}^2}{{\cosh \left(2x\right)}-1}}
2687\frac{5}{2}
2688\frac{2}{5}
2689\frac{2}{25}
2690\frac{25}{2}
2691{\lim_{x\to x_0} f\left(x\right)}
2692x_0
2693f\left(x\right)
2694f\left(x\right)
2695x_0
2696x_0
2697f\left(x\right)
2698f\left(x\right)
2699x_0
2700f\left(x\right)
2701x_0
2702x_0
2703A
2704x_0
2705A
2706x_0
2707A
2708x_0
2709A
2710x_0
2711A
2712x_0
2713A
2714{\lim_{x\to +\infty } f\left(x\right)}=l
2715f\left(x\right)
2716y=l
2717f\left(x\right)
2718y=l
2719f\left(x\right)
2720x=l
2721f\left(x\right)
2722f\left(x\right)
2723{\lim_{x\to +\infty } f\left(x\right)}=-\infty
2724f\left(x\right)
2725f\left(x\right)
2726f\left(x\right)
2727f\left(x\right)
2728f\left(x\right)
2729y={\sin e^{-x}}
2730x\to 0^+
2731x\to 0^-
2732x\to +\infty
2733x\to -\infty
2734{\lim_{x\to 0} {\sin \left(\frac{1}{x}\right)}}
27350
27361
2737\pi
2738\infty
2739y={\ln {\arctan \left(x^2\right)}}
2740\mathbb{R}
2741\left(-\infty ,0\right)
2742\left(0,+\infty \right)
2743f
2744x_0
2745x_0
2746x_0
2747x_0
2748x_0
2749x_0
2750f
2751x_0
2752x_0
2753x_0
2754x_0
2755x_0
2756x_0
2757f
2758f^{'}\left(x_0\right)=0
2759f^{''}\left(x_0\right)>0
2760x_0
2761f
2762x_0
2763f
2764x_0
2765f
2766x_0
2767f
2768x_0
2769f
2770x_0
2771f
2772f^{'}\left(x\right)=0
2773\exists \varepsilon :\ \forall x\left|x-x_0\right|<\varepsilon \Rightarrow f\left(x\right)
2774\exists \varepsilon :\ \forall x\left|x-x_0\right|<\varepsilon \Rightarrow f\left(x\right)\le f\left(x_0\right)
2775\exists \varepsilon :\ \forall x\left|x-x_0\right|<\varepsilon \Rightarrow f\left(x\right)>f\left(x_0\right)
2776\exists \varepsilon :\ \forall x\left|x-x_0\right|<\varepsilon \Rightarrow f\left(x\right)\ge f\left(x_0\right)
2777f:\left[a,b\right]\to \mathbb{R}
2778f\left(a\right)f\left(b\right)<0
2779x_0\in \left[a,b\right]
2780f\left(x_0\right)=0
2781x_0\in \left[a,b\right]
2782f\left(x_0\right)\neq 0
2783x_0\in \left[a,b\right]
2784f\left(x_0\right)=0
2785x_0\in \left[a,b\right]
2786f\left(x_0\right)\neq 0
2787x_0\in \left[a,b\right]
2788f\left(x_0\right)=0
2789f:A\to \mathbb{R}
2790A\subseteq \mathbb{R}
2791f
2792A
2793f
2794A
2795A
2796f
2797A
2798A
2799f
2800A
2801A
2802f
2803A
2804f
2805A
2806y=2\left|{\sin x}\right|-2
2807x=0
2808x=\frac{\pi }{2}
2809x=k\pi
2810k\in \mathbb{N}
2811x=\frac{\pi }{2}+k\pi
2812k\in \mathbb{N}
2813f\left(x\right)={\sin x}
2814g\left(x\right)={\cos x}
2815x\in \left[0,2\pi \right]
2816f\left(x\right)=e^x
2817g\left(x\right)=-{\arctan x}
2818\mathbb{R}
2819f\left(x\right)>g\left(x\right)\ \forall x\in \mathbb{R}
2820f\left(x\right)\le g\left(x\right)\ \forall x\in \mathbb{R}
2821y
2822f\left(x\right)=e^x
2823g\left(x\right)={\cos x}
2824f\left(x\right)\ge g\left(x\right)\ \forall x
2825f\left(x\right)\le g\left(x\right)\ \forall x
2826f\left(x\right)>g\left(x\right)\ \forall x\ge 0
2827f\left(x\right)\ge g\left(x\right)\ \forall x\ge 0
2828f:\mathbb{R}\to \mathbb{R}
2829f:{\mathbb{R}}^2\to \mathbb{R}
2830f:X\to Y
2831x\in X
2832y\in Y
2833x\in X
2834y\in Y
2835y\in Y
2836x\in X
2837y\in Y
2838x\in X
2839y\in Y
2840x\in X
2841f
2842x_0
2843f
2844x_0
2845f
2846x_0
2847f
2848x_0
2849f^{''}
2850x_0
2851f^{''}
2852x_0
2853f:X\to \mathbb{R}
2854X
2855X
2856f\left(X\right)\subseteq \mathbb{R}
2857f\left(X\right)\subseteq \mathbb{R}
2858f\left(X\right)\subseteq \mathbb{R}
2859f:X\to \mathbb{R}
2860X
2861X
2862f\left(X\right)\subseteq \mathbb{R}
2863f\left(X\right)\subseteq \mathbb{R}
2864f:X\to \mathbb{R}
2865f
2866f
2867f
2868f
2869{\lim_{x\to x_0} f\left(x\right)}
2870x\to x^+_0
2871x\to x^-_0
2872x\to x^+_0
2873x\to x^-_0
2874x\to x^+_0
2875x\to x^-_0
2876x\to x^+_0
2877x\to x^-_0
2878f\left(x_0\right)
2879x\to x_0
2880f\left(x\right)
2881x_0
2882x\to x_0
2883f\left(x\right)
28840
2885x\to x_0
2886f\left(x\right)
2887+\infty
2888x\to x_0
2889f\left(x\right)
2890-\infty
2891x\to x_0
2892f\left(x\right)
28931
2894x\to x_0
2895x\to x_0
2896f\left(x\right)
2897x\_0
2898x\to x_0
2899f\left(x\right)
29000
2901x\to x_0
2902f\left(x\right)
2903\infty
2904x\to x_0
2905f\left(x\right)
29061
2907x\to x_0
2908f\left(x\right)
2909f\left(x_0\right)
2910x\to x_0
2911{\lim_{x\to x_0} \frac{f\left(x\right)}{g\left(x\right)}}
2912x\neq 0
2913x_0\neq 0
2914g\left(x_0\right)\neq 0
2915g\left(x\right)\neq 0\ \forall x
2916g\left(x\right)\neq 0
2917x\to x_0
2918f\left(x\right)
2919g\left(x\right)
2920x\to x_0
2921f
2922g
2923x\to x_0
2924{\lim_{x\to x_0} \frac{f\left(x\right)}{g\left(x\right)}}=0
2925{\lim_{x\to x_0} \frac{g\left(x\right)}{f\left(x\right)}}=0
2926{\lim_{x\to x_0} \frac{f\left(x\right)}{g\left(x\right)}}=l
2927{\lim_{x\to x_0} \frac{g\left(x\right)}{f\left(x\right)}}=l
2928{\lim_{x\to x_0} \frac{f\left(x\right)}{g\left(x\right)}}
2929g\left(x\right)
29300
2931x\to x_0
2932f\left(x\right)=o\left(g\left(x\right)\right)
2933{\lim_{x\to x_0} \frac{f\left(x\right)}{g\left(x\right)}}=0
2934{\lim_{x\to x_0} \frac{g\left(x\right)}{f\left(x\right)}}=1
2935{\lim_{x\to x_0} \frac{g\left(x\right)}{f\left(x\right)}}=l
2936{\lim_{x\to x_0} \frac{f\left(x\right)}{g\left(x\right)}}=+\infty
2937{\lim_{x\to x_0} \frac{f\left(x\right)}{g\left(x\right)}}=-\infty
2938f:\left[a,b\right]\to \mathbb{R}
2939\left[a,b\right]
2940\left(a,b\right)
2941c\in \left[a,b\right]:\frac{f\left(b\right)-f\left(a\right)}{b-a}=f^{'}\left(c\right)
2942c\in \left[a,b\right]:\frac{f\left(b\right)-f\left(a\right)}{b-a}=f\left(c\right)
2943c\in \left[a,b\right]:\frac{f\left(b\right)-f\left(a\right)}{b+a}=f\left(c\right)
2944c\in \left(a,b\right):\frac{f\left(b\right)-f\left(a\right)}{b-a}=f^{'}\left(c\right)
2945c\in \left(a,b\right):\frac{f\left(b\right)-f\left(a\right)}{b+a}=f\left(c\right)
2946x=0
2947y=\left|x\right|
2948y=x^{\frac{1}{3}}
2949y=\frac{1}{x}
2950y={\ln x}
2951x=0
2952y={\arctan x}
2953y=\sqrt{x}
2954y=\sqrt[3]{x}
2955y=\frac{1}{x}
2956y=\frac{\left|x\right|}{x-1}
2957x=0
2958x=1
2959x=0
2960x=1
2961x=1
2962x=0
2963x=0
2964x=1
2965x=1
2966x=0
2967y=\frac{\left|x-2\right|}{x+1}
2968x=2
2969y=0
2970y=\frac{1}{3}\left(x-2\right)
2971y=-\frac{1}{3}\left(x-2\right)
2972y=\frac{1}{3}\left(x-2\right)
2973y=-\frac{1}{3}\left(x-2\right)
2974y=\frac{\left|x-3\right|}{x}
2975x=3
2976f\left(x\right)=e^x
2977g\left(x\right)=x+k
2978k\in \mathbb{R}
2979\left(0,1\right)
2980k=0
2981k=1
2982k=e
2983k=\frac{1}{e}
2984k
2985f\left(x\right)=e^x
2986g\left(x\right)={\arctan \left(x+a\right)}+b
2987\left(0,1\right)
2988a=0
2989b=1
2990a=1
2991b=0
2992a
2993b=-{\arctan a}
2994b
2995a=-{\arctan b}
2996f\left(x\right)={\arctan x}
2997g\left(x\right)=ax^2
2998a=0
2999a=1
3000a={\arctan 1}
3001a={\tan 1}
3002f\left(x\right)
3003g\left(x\right)
3004\left(x_0,y_0\right)
3005f\left(x_0\right)=y_0
3006g\left(x_0\right)=y_0
3007f\left(x_0\right)=g\left(x_0\right)
3008f^{'}\left(x_0\right)=g^{'}\left(x_0\right)
3009f\left(x\right)=x^2-kx+1
3010k\in \mathbb{R}
3011y=x^2-1
3012y=1-x^2
3013y=1-\frac{1}{2}x^2
3014y=\frac{1}{2}x^2
3015y=-\frac{1}{2}x^2
3016y=mx+q
3017m,q\in \mathbb{R}
3018y=nx^2
3019n\in \mathbb{N}
3020t={\ln \left(x+k\right)}
3021k\in \mathbb{R}
3022D=\left\{x:x>0\right\}
3023C=\mathbb{R}
3024D=\mathbb{R}
3025C=\left\{y:y>0\right\}
3026D=\left\{x:x>k\right\}
3027C=\mathbb{R}
3028D=\mathbb{R}
3029C=\left\{y:y>k\right\}
3030D=\left\{x:x>k\right\}
3031C=\left\{y:y>k\right\}
3032f\left(x\right)=1-x^2
3033g\left(x\right)={\ln \left(x-k\right)}
3034\left(0,1\right)
3035k=0
3036k=1
3037k=e
3038k=1-e
3039f:\left(a,b\right)\to \mathbb{R}
3040f
3041x
3042{\lim_{h\to 0} \frac{f\left(x+h\right)-f\left(x\right)}{a-b}}
3043{\lim_{x\to h} \frac{f\left(x+h\right)-f\left(x\right)}{a-b}}
3044{\lim_{h\to 0} \frac{f\left(x+h\right)-f\left(x\right)}{h}}
3045{\lim_{x\to h} \frac{f\left(x+h\right)-f\left(x\right)}{b-a}}
3046{\lim_{x\to h} \frac{f\left(x+h\right)-f\left(x\right)}{h}}
3047f
3048x_0
3049f
3050x_0
3051f
3052x_0
3053f
3054x_0
3055f
3056x_0
3057f
3058x_0
3059f
3060x_0
3061f
3062x_0
3063x\to 0
3064f^{'}\left(x\right)
3065m
3066n
3067m\neq n
3068x_0
3069f
3070x_0
3071f
3072x_0
3073f^{'}
3074x_0
3075f
3076x_0
3077f^{'}
3078n-
3079f\left(x\right)={\sin x}
3080n=4k+3
3081k\in \mathbb{N}
3082f^{\left(n\right)}\left(x\right)={\sin x}
3083f^{\left(n\right)}\left(x\right)={\cos x}
3084f^{\left(n\right)}\left(x\right)=-{\sin x}
3085f^{\left(n\right)}\left(x\right)=-{\cos x}
3086k
3087f\left(x\right)={\sin \left(kx\right)}
3088k\in \mathbb{N}
3089x=0
30900
30911
3092\frac{\sqrt{2}}{2}
3093k
3094k^{13}
3095f\left(x\right)=e^{kx}
3096k\in \mathbb{R}
3097f^{\left(n\right)}\left(x\right)=ke^x
3098f^{\left(n\right)}\left(x\right)=ke^{kx}
3099f^{\left(n\right)}\left(x\right)=ne^{\left(n-1\right)kx}
3100f^{\left(n\right)}\left(x\right)=k^ne^x
3101f^{\left(n\right)}\left(x\right)=k^ne^{kx}
3102f\left(x\right)=\frac{ax}{x-b}
3103a,b\in \mathbb{R}
3104f^{'}\left(x\right)=\frac{a\left(2x-b\right)}{x-b}
3105f^{'}\left(x\right)=\frac{a\left(2x-b\right)}{{\left(x-b\right)}^2}
3106f^{'}\left(x\right)=-\frac{ab}{x-a}
3107f^{'}\left(x\right)=-\frac{ab}{{\left(x-b\right)}^2}
3108f^{'}\left(x\right)=\frac{ab}{{\left(x-a\right)}^2}
3109f\left(x\right)=xe^x
3110f^{\left(n\right)}\left(x\right)=e^x\left(x+1\right)
3111f^{\left(n\right)}\left(x\right)=nxe^x
3112f^{\left(n\right)}\left(x\right)=\left(x+n\right)e^x
3113f^{\left(n\right)}\left(x\right)=n\left(x+n\right)e^x
3114f^{\left(n\right)}\left(x\right)=e^{x+n}
3115f
3116f\left(a\right)<0
3117f\left(b\right)>0
3118\left(a,b\right)
3119\left(a,b\right)
3120\left(a,b\right)
3121\left(a,b\right)
3122f\left(x\right)
3123f\left(0\right)=f\left(2\right)=f\left(4\right)=
3124f\left(x\right)
3125\left(0,2\right)
3126\left(2,4\right)
3127f\left(x\right)
3128\left(0,2\right)
3129\left(2,4\right)
3130f\left(x\right)
3131x=0
3132x=2
3133x=4
3134f\left(x\right)
3135x=1
3136x=3
3137f\left(x\right)
3138x=2
3139f\left(x\right)={\ln \left(x-a\right)}
3140g\left(x\right)=x-b
3141a=b-1
3142b=a-1
3143a=b
3144b=-1
3145a=1
3146f
3147x_0
3148x\to x_0
3149f\left(x_0\right)=f\left(x\right)+f^{'}\left(x_0\right)\left(x-x_0\right)+o\left(x-x_0\right)
3150f\left(x\right)=f\left(x_0\right)+f^{'}\left(x_0\right)\left(x-x_0\right)+o\left(x-x_0\right)
3151f^{'}\left(x_0\right)=f\left(x_0\right)+f^{'}\left(x_0\right)+o\left(x-x_0\right)
3152f^{'}\left(x\right)=f\left(x\right)+f^{'}\left(x_0\right)\left(x-x_0\right)+o\left(x\right)
3153f\left(x\right)=f\left(x_0\right)+f^{'}\left(x_0\right)\left(x-x_0\right)+o\left(x_0\right)
3154f,g:\left(a,b\right)\to \mathbb{R}
3155n
3156x_0\in \left(a,b\right)
3157f
3158g
3159n
3160x_0
3161f^{\left(n\right)}\left(x\right)=g^{\left(n\right)}\left(x\right)
3162f
3163g
3164n
3165x_0
3166f^{\left(n\right)}\left(x\right)=g^{\left(n\right)}\left({x}_0\right)
3167f
3168g
3169n
3170x_0
3171f^{\left(i\right)}\left(x\right)=g^{\left(i\right)}\left(x_0\right)\ \forall i=0,\dots ,n
3172f
3173g
3174n
3175x_0
3176f^{\left(i\right)}\left(x_0\right)=g^{\left(i\right)}\left(x_0\right)\ \forall i=0,\dots ,n
3177f
3178g
3179n
3180x_0
3181f^{\left(i\right)}\left(x_0\right)=g^{\left(i\right)}\left(x_0\right)\ \forall i=0,\dots ,n
3182P\left(x\right)=f\left(x_0\right)+f^{'}\left(x_0\right)\left(x-x_0\right)+o\left(x-x_0\right)
3183x\to x_0
3184f\left(x\right)
3185f\left(x\right)
3186f\left(x\right)
3187f\left(x\right)
3188f\left(x\right)\in C^2\left(\mathbb{R}\right)
3189x_0
3190f^{'}\left(x_0\right)=0
3191f^{''}\left(x_0\right)\neq 0
3192x_0
3193x_0
3194f^{\left(n\right)}\left(x_0\right)<0
3195x_0
3196f^{''}\left(x_0\right)<0
3197x_0
3198x_0
3199f\left(x\right)\in C^{\infty }\left(\mathbb{R}\right)
3200\ \forall x\in \mathbb{R}
3201\ \forall x\in \mathbb{R}
3202\ \forall x\in \mathbb{R}
3203\ \forall x\in \mathbb{R}
3204f\left(x\right)\in C^{\infty }\left(\mathbb{R}\right)
3205x_0
32068
3207f\left(x\right)
3208x_0
3209f^{\left(9\right)}\left(x_0\right)=0
3210x_0
3211f
3212f^{\left(9\right)}\left(x_0\right)>0
3213x_0
3214f
3215f^{\left(9\right)}\left(x_0\right)<0
3216x_0
3217f
3218f^{\left(9\right)}\left(x_0\right)\neq 0
3219x_0
3220f
3221{\ln \left(1+x\right)}
3222x-x^2+x^3+o\left(x^3\right)
3223x-\frac{1}{2}x^2+\frac{1}{3}x^3+o\left(x^3\right)
3224x-\frac{1}{2!}x^2+\frac{1}{3!}x^3+o\left(x^3\right)
3225x+\frac{1}{2!}x^2-\frac{1}{3!}x^3+o\left(x^3\right)
32261+x-\frac{1}{2!}x^2+\frac{1}{3!}x^3+o\left(x^3\right)
3227{\cos x}
32281-\frac{1}{2}x^2+\frac{1}{4}x^4+o\left(x^4\right)
3229x-\frac{1}{3!}x^3+o\left(x^4\right)
32301-\frac{1}{2!}x^2+\frac{1}{4!}x^4+o\left(x^4\right)
32311-\frac{1}{2!}x^2+\frac{1}{4!}x^4
32321-\frac{1}{2!}x^2+o\left(x^4\right)
3233f\left(x\right)={\sin x}-{\cosh x}
3234f
3235y
3236f
3237y
3238f
3239f
3240f
3241\frac{2}{1+e^x}
32421+x+x^3+o\left(x^3\right)
32431-x+x^3+o\left(x^3\right)
32441+\frac{x}{2}+\frac{x^3}{24}+o\left(x^3\right)
32451-\frac{x}{2}+\frac{x^3}{24}+o\left(x^3\right)
32461-\frac{x}{2}+\frac{x^3}{24}-\frac{x^5}{240}+o\left(x^5\right)
3247f\left(x\right)={\arctan \sqrt{\frac{1-{\cos x}}{1+{\cos x}}}}
3248x=\frac{\pi }{2}+2k\pi
3249f\left(x\right)=k{\left(x-a\right)}^3
3250+\infty
3251x\to +\infty
3252-\infty
3253x\to +\infty
3254k<0
3255-\infty
3256x\to -\infty
3257k<0
3258+\infty
3259x\to +\infty
3260a<0
3261+\infty
3262x\to -\infty
3263a>0
3264f\left(x\right)=\left(x-a\right)\left(x-b\right)\left(x-c\right)
3265a,b,c\in \mathbb{R}
3266a\le b\le c
32673
32683
3269f\left(x\right)=k{\cos \left(kx\right)}
3270k\in \mathbb{R}
3271k
3272k
3273k
3274k
3275f\left(x\right)=e^{-x{\sin x}}
3276g\left(x\right)=-x{\sin \left(kx\right)}
3277g\left(x\right)=-x{\sin \left(kx\right)}
3278g\left(x\right)=x{\sin \left(kx\right)}
3279g\left(x\right)=x{\sin \left(kx\right)}
3280f:\left[a,b\right]\to \mathbb{R}
3281f:\left[a,b\right]\to \mathbb{R}
3282f\left(x\right)=\frac{1}{\sqrt{x}}-2e^x+3
3283\int{f\left(x\right)dx}
3284\sqrt{x}-e^x + k
32852\left(\sqrt{x}-e^x\right) + k
32862\left(\sqrt{x}-e^x\right)+3 + k
32872\left(\sqrt{x}-e^x\right)+3x + k
32882\left(\sqrt{x}-e^x+3x\right) + k
3289f\left(x\right)={\ln x}
3290\int{f\left(x\right)dx}
3291{\ln x}+k
3292{\ln x}-1+k
3293{\ln x}+1+k
3294x\left({\ln x}-1\right)+k
3295x\left({\ln x}+1\right)+k
3296f
3297g
3298f\le g
3299\int{f}>\int{g}
3300\int{f}\ge \int{g}
3301\int{f}<\int{g}
3302\int{f}\le \int{g}
3303\int{f}=\int{g}
3304f\left(x\right)
3305\left[a,b\right]
3306M={sup \left|f\left(x\right)\right|}
3307x\in \left[a,b\right]
3308\left|\int^b_a{f\left(x\right)dx}\right|=M\left(b-a\right)
3309\left|\int^b_a{f\left(x\right)dx}\right|\le M\left(b-a\right)
3310\left|\int^b_a{f\left(x\right)dx}\right|=M\left(a-b\right)
3311\int^b_a{f\left(x\right)dx}\le M\left(a-b\right)
3312\int^b_a{f\left(x\right)dx}=M\left(b-a\right)
3313\int{f}=\int{\left|f\right|}
3314\int{\left|f\right|}\le \int{f}
3315\left|\int{f}\right|\le \int{\left|f\right|}
3316\left|\int{f}\right| = \int{f}
3317\left|\int{f}\right|=\int{\left|f\right|}
3318f\left(x\right)
3319\left[a,b\right]
3320t\in \left[a,b\right]
3321\int^b_a{f\left(x\right)dx}=t\left(b-a\right)
3322\int^b_a{f\left(x\right)dx}=t\left(a-b\right)
3323\int^b_a{f\left(x\right)dx}=f\left(t\right)\left(b-a\right)
3324\int^b_a{f\left(x\right)dx}=f\left(t\right)\frac{1}{\left(a-b\right)}
3325\int^b_a{f\left(x\right)dx}=t\left(b-a\right)
3326f\left(x\right)
3327\left[a,b\right]
3328f
3329\left(b-a\right)\int^b_a{f\left(x\right)dx}
3330\frac{1}{b-a}\int^b_a{f\left(x\right)dx}
3331\left(a-b\right)\int^b_a{f\left(x\right)dx}
3332\frac{1}{a-b}\int^b_a{f\left(x\right)dx}
3333f\left(x\right)
3334a
3335b
3336c
3337A=\int^b_a{f\left(x\right)dx}
3338B=\int^b_c{f\left(x\right)dx}
3339C=\int^c_a{f\left(x\right)dx}
3340A=B+C
3341B=A-C
3342C=A-B
3343f\left(x\right)\in C^0\left[a,b\right]
3344c\in \left[a,b\right]
3345F\left(x\right)=\int^x_c{f\left(t\right)dt}
3346F\in C^0\left[a,b\right]
3347f^{'}\left(x\right)=f\left(x\right)\ \forall x\in \left[a,b\right]
3348F\in C^1\left[a,b\right]
3349f^{'}\left(x\right)=f\left(x\right)\ \forall x\in \left[a,b\right]
3350F\in C^0\left[a,b\right]
3351F\left(x\right)=f^{'}\left(x\right)\ \forall x\in \left(a,b\right)
3352F\in C^1\left(a,b\right)
3353F\left(x\right)=f^{'}\left(x\right)\ \forall x\in \left(a,b\right)
3354F\in C^2\left(a,b\right)
3355f^{'}\left(x\right)=f\left(x\right)\ \forall x\in \left(a,b\right)
3356\int{f\left(x\right)dx}
3357f
3358f
3359f
3360f
3361f
3362f\left(x\right)={{\sin}^{2} x}
3363\int f\left(x\right)dx
3364{{\cos}^{2} x}+k
3365\frac{1}{2}{\cos 2x}+k
3366\frac{1}{2}\left(x-\cos 2x\right)+k
3367\frac{1}{2}\left(x-\sin x\cos x\right)+k
3368\frac{1}{2}\left(x-\sin 2x\cos 2x\right)+k
3369a,b,n\in \mathbb{R}
3370\int{na^b}da
3371a^b+k
3372\frac{na^b}{{\ln a}}+k
3373\frac{a^b}{{\ln a}}+k
3374\frac{n}{b+1}a^b+k
3375\frac{n}{b+1}a^{b+1}+k
3376a,b,c\in \mathbb{R}
3377\int{a^b{\cos c}}dc
3378\frac{a^{b+1}}{b+1}\cos c
3379\frac{a^{b+1}}{b+1}\sin c
3380a^b \sin c
3381\frac{a^b}{\ln a} \cos c
3382\frac{a^{b+1}}{{\ln a}}{\sin c}
3383f\left(x\right)={{\tan}^{2} x}
3384\int{f\left(x\right)dx}
3385{\tan x}+k
3386{{\tan}^{2} x}+k
3387{\tan x}-x+k
3388{\tan x}+x+k
3389{\tan x}+x^2+k
3390f\left(x\right)=\frac{\sqrt{1+x}}{\sqrt{1-x}}+\frac{\sqrt{1-x}}{\sqrt{1+x}}
3391\int{f\left(x\right)dx}
3392{\arcsin x}+k
3393{\arccos 2x}+k
33942{\arccos 2x}+k
33952{\arcsin x}+k
3396{{\arcsin}^{2} 2x}+k
3397f\left(x\right)=\frac{3}{x{\ln x}}
3398\int{f\left(x\right)dx}
3399{\ln {\ln x}}+k
3400{\ln \left|{\ln x}\right|}+k
3401{\ln {{\ln}^{2} x}}+k
34023\ln {\ln x}+k
34033\ln \left|{\ln x}\right|+k
3404f\left(x\right)=\frac{e^{\frac{1}{x}}}{x^2}
3405\int{f\left(x\right)dx}
3406e^{2x}+k
3407e^{\frac{1}{x}}+k
3408-e^{\frac{1}{x}}+k
3409e^{\frac{1}{x^2}}+k
3410-2e^{\frac{1}{x}}+k
3411f\left(x\right)=\frac{x}{x-7}
3412\int{f\left(x\right)dx}
3413x+{\ln \left|x+7\right|}+k
3414x-7 \ln \left|x+7\right| +k
3415x+7 \ln \left|x-7\right| +k
34167\left(x-{\ln \left|x+7\right|}\right)+k
34177\left(x+{\ln \left|x-7\right|}\right)+k
3418f\left(x\right)=\frac{7}{{\sin x}}
3419\int{f\left(x\right)dx}
3420{\tan {\ln \left|\frac{x}{2}\right|}}+k
3421{\ln \left|{\cos x}\right|}+k
3422{\ln \left|7{\cos x}\right|}+k
34237{\ln \left|{\tan \frac{x}{2}}\right|}+k
3424{\tan \left(7{\ln \left|\frac{x}{2}\right|}\right)}+k
3425f\left(x\right)=\frac{x^4+x^3+6}{x^2+x}
3426\int{f\left(x\right)dx}
3427x^3+3{\ln \left|\frac{x}{x+1}\right|}+k
3428\frac{1}{3}\left(x^3+6{\ln \left|\frac{x}{x+1}\right|}\right)+k
3429\frac{1}{3}\left(x^3+18{\ln \left|\frac{x}{x+1}\right|}\right)+k
34303\left(x^3+\frac{1}{3}{\ln \left|\frac{x}{x+1}\right|}\right)+k
34313\left(\frac{1}{3}x^3+18{\ln \left|\frac{x}{x+1}\right|}\right)+k
3432f\left(x\right)=\frac{1}{1+e^x}
3433\int{f\left(x\right)dx}
3434x+{\ln \left(e^x+1\right)}+k
3435{\ln \left(e^x+1\right)}+k
3436x-{\ln \left(e^x+1\right)}+k
3437-{\ln \left(e^x+1\right)}+k
3438{\ln \left(e^x+1\right)}-x+k
3439f\left(x\right)=\frac{{\cos {\ln x}}}{x}
3440\left(e^{\frac{\pi }{2}},1\right)
3441{\cos {\ln \left|x\right|}}+e
3442{\sin {\ln \left|x\right|}}
3443{\ln \left|{\cos x}\right|}+\pi /2
3444{\cos {\ln \left|x\right|}}
3445{\ln \left|{\sin x}\right|}+1
3446f\left(x\right)=\frac{k}{x^2+4}
3447k\in \mathbb{R}
3448g\left(x\right)=2{arctan f\left(x\right)}+k
3449\int{f\left(x\right)dx}=g\left(x\right)
3450k=2
3451f\left(x\right)=2x
3452k=\frac{1}{2}
3453f\left(x\right)=x
3454k=-4
3455f\left(x\right)=-\frac{x}{2}
3456k=4
3457f\left(x\right)=\frac{x}{2}
3458k=\frac{1}{4}
3459f\left(x\right)=\frac{x}{2}
3460f\left(x\right)=\frac{kx}{e^x}
3461k\in \mathbb{R}
3462g\left(x\right)=-\frac{k\left(x+1\right)}{e^x}+k
3463\int{f\left(x\right)dx}=g\left(x\right)
3464k=1
3465k=-1
3466k=e
3467k
3468k
3469f\left(x\right)=\frac{{\sin x}}{1-2{\cos x}}
3470\int{f\left(x\right)dx}
34712\left({\ln \left|f\left(x\right){\cos x}\right|}\right)+k
3472\frac{1}{2}\left({\ln \left|\frac{{\sin x}}{f\left(x\right)}\right|}\right)+k
3473\frac{1}{2}\left({\ln \left|f\left(x\right)\right|}\right)+k
34742\left({\ln \left|2f\left(x\right){\cos x}\right|}\right)+k
34752\left({\ln \left|\frac{1}{f\left(x\right)}\right|}\right)+k
3476f\left(x\right)=\frac{x+2}{x-1}
3477\left[2,e+1\right]
3478\frac{1+e}{e-1}
3479\frac{2+e}{e-2}
3480\frac{1+e}{2-e}
3481\frac{2+e}{e-1}
3482\frac{2+e}{1-e}
3483f\left(x\right)=\frac{x}{1+x^2}
3484\left[0,2\right]
3485\frac{{\ln 5}}{2}
3486\frac{{\ln 5}}{4}
3487\frac{{\ln 5}}{8}
3488\frac{{\ln 5}}{2}
3489\frac{{\ln 5}}{5}
3490f\left(x\right)=\frac{k}{\sqrt{x}}
3491k\in \mathbb{R}
3492\frac{12}{5}
3493\left[4,9\right]
3494k=1
3495k=2
3496k=3
3497k=6
3498k=12
3499\frac{1}{2}{\sin 4x}
3500\left\{a_n\right\}
3501a_n
3502\left\{s_n\right\}
3503s_n=\sum^{\infty }_{n=0}{{\left(a_n\right)}^2}
3504s_n=\sum^{\infty }_{n=0}{a_n}
3505s_n=\prod^{\infty }_{n=0}{\frac{1}{a_n}}
3506s_n=\sum^{\infty }_{n=0}{\sqrt{a_n}}
3507s_n={\lim_{n\to +\infty } a_n}
3508\left\{a_n\right\}
3509s_n = \sum_{k=1}^n a_k
3510a_n
3511a_n
3512a_n
3513a_n
3514n-
3515s_n
3516a_n
3517\left\{a_n\right\}
3518\left\{a_n\right\}
3519\left\{s_n\right\}
3520\left\{s_n\right\}
3521\left\{s_n\right\}
3522\left\{a_n\right\}
3523\left\{s_n\right\}
3524a_n
3525\left\{s_n\right\}
3526\left\{a_n\right\}
3527\left\{s_n\right\}
3528\left\{a_n\right\}
3529\left\{s_n\right\}
3530\left\{a_n\right\}
3531\left\{s_n\right\}
3532\left\{s_n\right\}
3533\left\{s_n\right\}
3534\left\{s_n\right\}
3535\left\{s_n\right\}
3536\left\{s_n\right\}
3537\sum^{\infty }_{n=0}{a_n}
3538\sum^{\infty }_{n=0}{{\left(a_n\right)}^2}
3539\sum^{\infty }_{n=0}{\frac{1}{a_n}}
3540\sum^{\infty }_{n=0}{\left(a_n-a_{n+1}\right)}
3541\sum^{\infty }_{n=0}{\left(a_n-a_{n+2}\right)}
3542\sum^{\infty }_{n=0}{a_n}
3543\varepsilon >0
3544N
3545\ \forall i\ge 0
3546\ \forall j\ge n
3547\left|a_i+a_{i+1}+...+a_{i+j}\right|<\varepsilon
3548\varepsilon >0
3549N
3550\ \forall i\ge 0
3551\ \forall j\ge n
3552\left|a_i+a_{i+1}+...+a_{i+j}\right|>\varepsilon
3553\varepsilon >0
3554N
3555\ \forall i\ge N
3556\ \forall j\ge 0
3557\left|a_i+a_{i+1}+...+a_{i+j}\right|<\varepsilon
3558\varepsilon >0
3559N
3560\ \forall i\ge N
3561\ \forall j\ge 0
3562\left|a_i+a_{i+1}+...+a_{i+j}\right|>\varepsilon
3563\sum^{\infty }_{n=1}{n}
3564\sum^{\infty }_{n=1}{n^2}
3565\sum^{\infty }_{n=1}{\frac{1}{n}}
3566\sum^{\infty }_{n=1}{\frac{1}{n^2}}
3567\sum^{\infty }_{n=1}{\frac{1}{\sqrt{n}}}
3568\sum^{\infty }_{n=0}{a_n}
3569\sum^{\infty }_{n=0}{b_n}
3570a_n\sim b_n
3571b_n
3572a_n\sim b_n
3573b_n
3574a_n
3575a_n\sim b_n
3576b_n
3577a_n
3578a_n\sim b_n
3579b_n
3580a_n
3581a_n\sim b_n
3582\sum^{\infty }_{n=0}{a_n}
3583{\lim_{n\to +\infty } \frac{a_{n+1}}{a_n}}=l
3584l<1
3585l\ge 1
3586l\le 1
3587l>1
3588l\le 1
3589\sum^{\infty }_{n=0}{a_n}
3590\sum^{\infty }_{n=0}{\left|a_n\right|}
3591\sum^{\infty }_{n=0}{\left|a_n\right|}
3592\sum^{\infty }_{n=0}{a_n}
3593\sum^{\infty }_{n=0}{a_n}
3594\sum^{\infty }_{n=0}{\left|a_n\right|}
3595\sum^{\infty }_{n=0}{\left|a_n\right|}
3596\sum^{\infty }_{n=0}{a_n}
3597\sum^{\infty }_{n=0}{a_n}
3598\sum^{\infty }_{n=0}{\left|a_n\right|}
3599\sum^{\infty }_{n=0}{\left|a_n\right|}
3600\sum^{\infty }_{n=0}{\frac{1}{\left|a_n\right|}}
3601\sum^{\infty }_{n=0}{\frac{1}{\left|a_n\right|}}
3602\sum^{\infty }_{n=1}{\frac{1}{n^k}}
3603k=1
3604k>1
3605k=0
3606k>0
3607k>=1
3608\sum^{\infty }_{n=1}{\frac{n+e^{-n}}{n^2-\ln\left(n\right)}}
3609\sum^{\infty }_{n=1}{\frac{2^n}{3^n-n}}
3610\sum^{\infty }_{n=1}{\frac{n!}{n^n}}
3611\sum^{\infty }_{n=1}{\frac{\left(2n\right)!}{{\left(n!\right)}^2}}
3612\sum^{\infty }_{n=1}{\frac{1+{\cos n}}{n^2}}
3613\sum^{\infty }_{n=1}{\frac{k^n}{n^2}}
3614k>1
3615k<1
3616k\le 1
3617k\ge 1
3618k=1
3619\sum^{\infty }_{n=1}{{\left(\ln\left(\frac{4n+5}{3n-2}\right)\right)}^n}
3620\sum^{\infty }_{n=1}{\frac{{\cos n}}{n^2-2n-3}}
3621A=\sum^{\infty }_{n=1}{\frac{4}{n+{\ln n}}}
3622B=\sum^{\infty }_{n=1}{\frac{e^n}{{\sinh n}}}
3623C=\sum^{\infty }_{n=1}{\frac{e^n}{2^n+5^n}}
3624A
3625C
3626A
3627B
3628B
3629A
3630A
3631B
3632C
3633B
3634A
3635C
3636A=\sum^{\infty }_{n=1}{\frac{1}{n^5{\ln n}}}
3637B=\sum^{\infty }_{n=1}{\frac{1}{{\ln \left(n+1\right)}}}
3638C=\sum^{\infty }_{n=1}{\frac{n}{n^2+1}}
3639A
3640B
3641C
3642C
3643B
3644B
3645C
3646A
3647B
3648C
3649B
3650A
3651C
3652F\left(x\right)=\int^x_a{\frac{2{\sin t}}{1+t}dt}
3653\left(-\infty ,-1\right]\cup \left[-1,+\infty \right)
3654\left(-\infty ,-1\right)\cup \left(-1,+\infty \right)
3655\left(-\infty ,-1\right]
3656\left(-1,+\infty \right)
3657\left(-\infty ,-1\right)
3658\int^{+\infty }_0{xe^{-x}}dx
3659e
36602e
3661\frac{2}{e}
36621
3663+\infty
3664{\lim_{x\to +\infty } \frac{1}{x^2}\int^x_1{\left(t+\frac{1}{t}\right)dt}}
36650
36661
36672
3668\frac{1}{2}
3669+\infty
3670f
3671\mathbb{R}
3672F\left(x\right)=\int^x_0{f\left(t\right)dt}
3673{\lim_{x\to +\infty } F\left(x\right)}
3674{\lim_{x\to +\infty } F\left(x\right)}=+\infty
3675{\lim_{x\to +\infty } F\left(x\right)}=0
3676F\left(-1\right)=0
3677F
3678\mathbb{R}
3679\int^{+\infty }_{-\infty }{\frac{\left|x\right|}{9x^2+1}dx}
36800
36811
3682\pi
3683e
3684+\infty
3685\int^{+\infty }_{-\infty }{\frac{1}{x^2+1}dx}
3686\pi
3687\frac{\pi }{2}
3688\frac{\pi }{4}
36890
3690+\infty
3691f:\mathbb{R}\to \mathbb{R}
3692f\left(x\right)=-f\left(-x\right)
3693\int^1_0{f\left(x\right)dx}=0
3694\int^1_{-1}{f\left(x\right)dx}=0
3695\int^1_{-1}{f^2\left(x\right)dx}=0
3696\int^1_{-1}{f\left(x\right)dx}=2\int^1_{-1}{f\left(x\right)dx}
3697\int^1_{-1}{f\left(x\right)dx}=2\int^1_0{f^2\left(x\right)}dx
3698f:\mathbb{R}\to \mathbb{R}
3699\int^3_{-1}{f\left(x\right)dx}=8
3700x_0\in \left[-1,3\right]
3701f\left(x_0\right)=1
3702f\left(x_0\right)=2
3703f\left(x_0\right)=3
3704f\left(x_0\right)=\frac{1}{2}
3705f\left(x_0\right)=\frac{1}{3}
3706z
3707z+\overline{z}=0
3708z
3709\left|z\right|=\left|z-1\right|
3710z
3711\left|z\right|-2<0
3712z
3713\left|z\right|-2\ge 0
3714{\lim_{x\to +\infty } \frac{2x+5{\ln x}}{4x+3{\ln x}}}
37150
37161
37172
3718\frac{1}{2}
3719+\infty
3720{\ln x}=4-x^2
37210
37221
37232
37243
3725{\arctan x}=2-e^x
37260
37271
37282
37293
3730{\tan x}={\cos x}
37310
37321
37332
37343
3735k
3736{\ln x}=kx
37370
37380
37390
37400
37410
3742f\left(x\right)=x^3-5x^2+8x-4
3743x
3744f:\mathbb{R}\to \mathbb{R}
3745x=0
3746x=2
3747x=4
3748f^{'}
3749f
3750f^{'}
3751f
3752f^{'}
3753f\left(x\right)=\left\{ \begin{array}{c} {\sin \left(\frac{\pi }{2}x\right)}x<-1 \\ \left|x\right|+kx\ge -1 \end{array}\right.
3754x=-1
3755k=0
3756k=1
3757k=-1
3758k=2
3759k=-2
3760f:\mathbb{R}\to \mathbb{R}
3761f
3762f^{'}\left(x_0\right)=f^{''}\left(x_0\right)=0
3763x_0
3764f\left(x\right)>0
3765x
3766{\mathop{lim}_{x\to -\infty } f\left(x\right)}={\mathop{lim}_{x\to +\infty } f\left(x\right)}=0
3767f
3768\mathbb{R}
3769f
3770x_0
3771f
3772f^{''}\left(x_0\right)<0
3773f
3774x_0
3775f
3776f^{''}\left(x_0\right)>0
3777f
3778f^{''}\left(x_0\right)<0
3779x_0
3780z
3781\left(z-\overline{z}\right)\overline{z}=2
3782f\left(x\right)=x^2-3x+5
3783g\left(x\right)=2x^2+3x-1
37840
37851
37862
37873
3788f\left(x\right)=\frac{1}{x^2-3x+5}
3789g\left(x\right)=e^x
37900
37911
37922
37933
3794x{\cos \left(2x\right)}=500
3795f\left(x\right)=\left|x^2-4x-5\right|
3796\left[-2,-4\right]
3797-1
37982
37992
3800-1
38015
38022
38037
380427
38059
38060
3807y=e^x{\ln \left(3-x\right)}
3808y=\frac{\sqrt{x}}{e^x}
3809x\ge 0
3810\infty
3811x\to +\infty
3812\lim\limits_{x\to+\infty} f(x) = 4
3813f(x)
3814\lim\limits_{x\to -\infty} f(x) =
3815- \infty
38160
38174
3818-4
3819- \infty
3820f: A\to A
3821A
3822f^{-1}: A\to A
3823\lim\limits_{x \to a^-} f(x) = 2
3824\lim\limits_{x\to a^+} f(x) = -\infty
3825f
3826x=a
3827f
3828x=a
3829y=f(a)
3830f
3831f
3832x=a
3833y=f(a)
3834f
3835\mathbb{R}
3836\mathbb{N}
3837\mathbb{N}
3838\mathbb{R}
3839f(x)=\sin(x)+\cos(x)
3840f(x)=\sin(x)-\cos(x)
3841f(x)=\tan(x)
3842f(x)=\cos(x)-\sin(x)
3843f(x)=1
3844f(x)=2\sin(x)
3845f: \left[a, b\right]\to\mathbb{R}
3846f(x)=\ln(-x)
3847f(x)
3848f(x)
3849f(x)
3850f(x)
3851f(x)=\ln(3x^2)
3852f(x)
3853f(x)
3854f(x)
3855f(x)
3856f(x)
3857\ln(a\cdot b)=\ln(a)\cdot\ln(b)
3858\ln(a+b)=\ln(a)\cdot\ln(b)
3859\ln(\frac a b)=\frac{\left[\ln(a)+\ln(b)\right]}{2}
3860\ln(a\cdot b)=\ln(a)+\ln(b)
3861\ln(a-b)=\frac {\ln(a)}{\ln(b)}
3862f: \left[2, 3\right]\to\mathbb{R}
3863f(x)=6x^2
3864f
386538
386644
386754
3868f(x)
3869\frac {f^{'}(x)}{f(x)}
3870e^{f(x)}+c
3871\sin f(x)+c
3872\tan f(x)+c
3873\arcsin f(x)+c
3874\ln f(x) +c
3875f(x): \mathbb{R}\to\mathbb{R}
3876x=b
3877f(x)
3878x=b
3879f(x)
3880x=b
3881f(x)
3882x=b
3883f(x)
3884x=b
3885f(x)=\sin(2x)^2
3886f(x)
38872\pi
3888f(x)
3889\pi
3890f(x)
3891x=0
3892f(x)
3893x\to +\infty
3894f(x)=\frac{1-\cos x}{x}
3895\lim\limits_{x \to 0} f(x)^2=1
3896\lim\limits_{x \to \pi} f(x)=\frac 1 2
3897\lim\limits_{x \to 0} f(x)=\frac 1 2
3898\lim\limits_{x \to \pi} f(x)=0
3899\lim\limits_{x \to0} f(x)=0
3900\frac{x+2}{\ln(x-4)}
3901x=0
3902x=5
3903x=5
3904x=0
3905x=5
3906\mathbb{R}
3907\mathbb{R}
3908f(x)=e^{\left(x^2\right)}
3909f(x)=\sin\left(x^2\right)
3910f(x)=\ln\left[\left(x+2\right)^2\right]
3911f(x)=(x-3)^3
3912f(x)=|x|
3913f(x)=x^2-3x
3914\left[2, 3\right]
3915x=3
3916f(x)=e^{\ln\left[\left(x^2-9\right)^2\right]}
3917f(x)=\frac{2x-6}{x+3}
3918f(x)=\ln(x-2)
3919n
3920\mathbb{Q}
3921\mathbb{N}
3922\mathbb{R}
3923\mathbb{Q}
3924\mathbb{N}
3925f(x)=\sin\frac x 2
3926x\to +\infty
39270
39281
392943132
3930-1
3931-0.5
3932f: \left[a, b\right]\to\mathbb{R}
3933f
3934f
3935f
3936f
3937f\left(x\right)=\ln\left(x^2 \right)+\ln\left(x-3 \right)
3938\left(-\infty,+\infty\right)
3939\left(-\infty,3\right]
3940\left[3,+\infty\right)
3941\left(-\infty,3\right)
3942\left(3,+\infty\right)
3943f(x): I\to \mathbb{R}
3944f
3945f
3946f
3947f
3948\left(1,+\infty\right)
3949f(x)=\ln(x)
3950-1
39511
3952f(n)=\frac{1}{n^{\frac 1 2}}
3953f
3954\left[a, b\right]\to \mathbb{R}
3955\sup(f)=M
3956\inf(f)=-M
3957f
3958f
3959f
3960f
3961f: \left[a, b\right] \mapsto \mathbb{R}
3962f
3963\left[a, b\right]
3964f
3965\left(a, b\right)
3966f
3967\left[a, b\right]
3968f
3969\left[a, b\right]
3970f(n)=\frac {n!}{n^2}
3971\frac 1 2
3972f(n)=\frac {(-1)^n}{n}
3973f(n)
3974n
39750
3976n
3977f(n)
39780
3979f(n)
39800
3981f(x)=\ln(x)
3982f(x)=\sin(x)
3983f(x)=e^{x^2}
3984\left(n\to+\infty\right)
3985n
39860
3987f(x)=a\cdot e^{2x}
3988f(x)
3989a
3990f^{'}(x)
3991a
3992f(x)
3993a
3994f^{'}(x)
3995a>0
3996f(x)
3997f^{'}(x)
3998f^{'}(x)
3999\frac 1 {n^{\frac 1 3}}
40001
40010
4002f^{'}(x)>0
4003f
4004f^{''}(x)
4005f(x)>f(x')
4006x>x'
4007f(x)
4008f(x)=\ln(x-1)
4009\ln(x)
4010z=4+i
401117
40125
4013\sqrt{5}
4014\sqrt{17}
4015z=3-5i
401634
4017\sqrt{8}
4018\sqrt{34}
40192
4020z=e^{2\pi i}
40212\pi
4022\sqrt{2\pi}
40231
4024\sqrt{2}
4025z=e^{\frac \pi 3 i}
4026\frac {\sqrt{3}} 2
4027\sqrt{3}
4028\pi
4029\frac \pi 3
4030\frac 3 \pi
4031f(x)=x
4032\log(x)
4033\mathbb{R}
4034\lim\limits_{n\to\infty} \left(1+\frac 1 n\right)^n
4035\sqrt{3}
4036e
4037\infty
40380
4039\lim\limits_{n\to\infty} \frac 1 n
4040\infty
40411
40420
4043f(x)=\log(x)
4044g(x)=x
4045x\to + \infty
4046f(x)\sim g(x)
4047f(x)=o(g(x))
4048g(x)=o(f(x))
4049f(x)=\sin(x)
4050g(x)=x
4051x\to+\infty
4052f(x)=o(g(x))
4053f(x)\sim g(x)
4054g(x)=o(f(x))
4055f(x)+g(x)=o(g(x))
4056f(x)=\sin(x)
4057g(x)=x
4058x\to 0
4059f(x)=o(g(x))
4060g(x)=o(f(x))
4061f(x)\sim g(x)
4062f(x)=\sqrt{x^2+x}
4063g(x)=x
4064x\to + \infty
4065f(x)=o(g(x))
4066g(x)=o(f(x))
4067f(x)-g(x)=0
4068f(x)\sim g(x)
4069\frac {f(x)}{g(x)} \sim 4
4070f
4071f
4072f
4073f
4074f
4075f
4076f
4077f
4078f
4079\left[a, b\right]
4080f(a)\cdot f(b)<0
4081f
4082x_0
4083f(x_0)=0
4084f
4085\left[a, b\right]
4086f(a)\cdot f(b)<0
4087\left[a, b\right]
4088f(a)=0
4089f(b)=1
40901
4091\frac 1 2
40920
4093\left[a, b\right]
4094f(a)=f(b)
4095x_0
4096f^{'}(x_0)=f(a)
4097f(x_0)=0
4098f^{''}(x_0)=0
4099f^{'}(x_0)=0
4100f(x)=\log(x)
4101g(x)=x^3
4102h(x)=3^x
4103x \to + \infty
4104g(x)
4105h(x)
4106f(x)
4107g(x)
4108f(x)=x^3
4109h(x)=x!
4110g(x)=3^x
4111x\to + \infty
4112h(x)
4113f(x)
4114g(x)
4115h(x)
4116h(x)=x^x
4117g(x)=x!
4118f(x)=3^x
4119x\to + \infty
4120g(x)
4121h(x)
4122f(x)
4123h(x)
4124e^x
41251+x
41261-x
41271+x^2
41281-x^2
4129\sin(x)
41301+x
41311-x
4132x
4133x^2
4134x^3
4135\sin(x)
4136x
41371+x^2
41381-x^2
4139x+x^2
4140x-x^2
4141\cos(x)
41421+\frac{x^2}{2}
4143 x^2
41441-\frac{x^2}{2}
4145h=2+4i
4146z=3+\sqrt{11}i
4147|h|>|z|
4148|z|>|h|
4149|h|=|z|
4150|h|+|z|=0
4151h=\sqrt{3}+2i
4152z=\sqrt{2}+5i
4153|z|>|h|
4154|z|<|h|
4155|z|=|h|
4156|z|+|h|=2
4157z=e^{i\pi}
41581
4159-1
41600
4161i
4162\pi
4163f
4164g
4165f+g
4166f+g
4167f+g
4168f
4169f
4170f
4171f^-1
4172f(x)=x^2
4173f
4174f
4175f
4176f(x)=x^3
4177f(x)=\cos(x)
4178\cos(x)
4179\sin(x)
4180\tan(x)
4181\cos(x)
4182\sin(x)
4183x^2
4184\ln(x)
4185\cos(x)
4186x^2
4187f
4188f^-1
4189\int_1^2 e^x \text{d}x
4190e^2
4191e^2 -1
4192e^2-e
4193e
4194\int_{1}^{2} e^x \text{d}x
4195e^2
41962+e
4197e
4198e^2-e
4199f(x)=|x|
4200f
4201f
4202f
4203f
4204f(x)=|\log(x)|
4205f
4206f
4207f
4208f
4209f
4210g
4211\mathbb{R}
4212f+3g
4213\mathbb{R}
4214f\cdot g
4215\mathbb{R}
4216f
4217g
4218f-g
4219\mathbb{R}
4220f
4221g
4222\mathbb{R}
4223\frac f g
4224f\cdot g
4225f+g
4226f
4227g
4228\mathbb{R}
4229f+g
4230\frac f g
4231f+g
4232f
4233g
4234\mathbb{R}
4235f+g
4236f+g
4237f+g
4238f
4239-f
4240f
4241-f
4242\int_1^\infty \frac 1 {x^2} \text{d}x
4243\int_1^\infty \frac 1 x \text{d}x
4244\int_0^1 \frac 1 {x^2} \text{d}x
4245\int_1^\infty \frac {1}{\sqrt{x}} \text{d}x
4246\int_1^\infty \cos(x) \text{d}x
4247f(x)=e^x
4248g(x)=x
4249x\to \infty
4250f(x)=o(g(x))
4251g(x)=o(f(x))
4252g(x)\sim f(x)
4253f(x)=x^2
4254g(x)=e^x
4255x\to \infty
4256f(x)=o(g(x))
4257g(x)=o(f(x))
4258g(x)\sim f(x)
4259f(x)=\log(x)
4260g(x)=x^x
4261x\to \infty
4262f(x)=o(g(x))
4263g(x)=o(f(x))
4264g(x)\sim f(x)
4265f(x)=\frac 1 {x^2}
4266g(x)=\frac 1 {x+x^2}
4267x\to \infty
4268f(x)=o(g(x))
4269g(x)=o(f(x))
4270g(x)\sim f(x)
4271f(x)=\sin(x)
4272g(x)=\cos(x)
4273x\to \infty
4274f(x)=o(g(x))
4275g(x)=o(f(x))
4276g(x)\sim f(x)
4277f(x)=\tan(x)
4278g(x)=\cos(x)
4279x\to \infty
4280f(x)=o(g(x))
4281g(x)=o(f(x))
4282g(x)\sim f(x)
4283f(x)=\sin(x)
4284g(x)=\tan(x)
4285x\to \infty
4286f(x)=o(g(x))
4287g(x)=o(f(x))
4288g(x)\sim f(x)
4289f(x)=3^x
4290g(x)=x^3
4291x\to \infty
4292f(x)=o(g(x))
4293g(x)=o(f(x))
4294g(x)\sim f(x)
4295f(x)=10^x
4296g(x)=x^x
4297x\to \infty
4298f(x)=o(g(x))
4299g(x)=o(f(x))
4300g(x)\sim f(x)
4301f(x)=\sin(x)
4302g(x)=x
4303x\to 0
4304f(x)=o(g(x))
4305g(x)=o(f(x))
4306g(x)\sim f(x)
4307f(x)=2-2\cos(x)
4308g(x)= x^2
4309x\to 0
4310f(x)=o(g(x))
4311g(x)=o(f(x))
4312g(x)\sim f(x)
4313f(x)=x
4314g(x)=x^3
4315x\to 0
4316f(x)=o(g(x))
4317g(x)=o(f(x))
4318g(x)\sim f(x)
4319f(x)=x
4320g(x)=\sqrt{x}
4321x\to 0
4322f(x)=o(g(x))
4323g(x)=o(f(x))
4324g(x)\sim f(x)
4325f
4326x_0
4327f^{'}(x_0)=0
4328x_0
4329f(x)=|x|
4330x_0=0
4331f(x)=1/x
4332x_0=0
4333f(x)=\sin(x)
4334\mathbb{R}
4335f(x)=\cos(x)
4336f(x)=\tan(x)
4337f(x)=e^x
4338f(x)=e^x
4339f(x)=x^2
4340f(x)=\log(x)
4341f(x)=\arctan(x)
4342f(x)=\arccos(x)
4343f(x)=\arcsin(x)
4344f(x)=x^3
4345I=\{x\in \mathbb{R}|x\geq 1\}
43460
4347I=\{x\in \mathbb{R}|x>a\}
4348a
4349I
4350I
4351I
4352I
4353I=\{x\in \mathbb{R}|x\geq a\}
4354a
4355I
4356I
4357I
4358I
4359I=\{x\in \mathbb{R}|x\in \mathbb{Q}\}
4360I
4361e
4362\sqrt{2}
4363\pi
43643+2i
4365e^{\ln{\frac 3 2}}
43662^\pi
4367\sqrt{2}
4368(-2)^\pi
4369\pi
4370\pi^2
4371\pi
43722^\pi
4373(-3)^{\sqrt{2}}
43740
4375\sqrt{\pi}
4376z=3+2i
4377\bar{z}
43783+2i
43793-2i
43802+3i
43812i
43823
4383z=5+2i
4384\bar{z}
43852+5i
43862-5i
43875+2i
43885-2i
43892
4390z
4391j=e+ei
4392n
4393n
4394\mathbb{C}
4395\mathbb{R}
4396\mathbb{N}
4397\mathbb{Q}
4398n
4399\mathbb{R}
4400n
4401n
4402(n-1)
4403z_0
4404-z_0
4405z_0^2
4406z_0^{-1}
4407\bar{z_0}
44080
4409f
4410I(x_0)
4411x_0
4412f(x_0)=0
4413f(0)=0
4414f^{'}(x_0)=0
4415f^{''}(x_0)=0
4416f
4417\left[a, b\right]
4418x_0
4419f^{'}(x_0)=\frac {f(b)-f(a)}{b-a}
4420f^{'}(x_0)=0
4421f(0)=\frac {f(b)-f(a)}{b-a}
4422f(1)=\frac {f(b)-f(a)}{b-a}
4423f(0)=\frac {f(x_0)-f(a)}{x_0-a}
4424\left[-1, 1\right]
4425x
4426\arcsin(x)
4427\arctan(x)
4428z^3
4429\left[-1, 1\right]
4430x
4431x e^x
4432\log(x+100)
4433x^2
4434\arctan(x)
4435\left[-1, 1\right]
4436\sin(x)
4437\cos(x)
4438x e^x
4439e^x
4440\tan(x)
4441\left[-1, 1\right]
4442|\tan(x)|
4443\cos(x)
4444x^2
4445\left[-1, 1\right]
4446\cos(x)
4447x^2
4448|\sin(x)|
4449\left[-1, 1\right]
4450\sqrt{x}
4451\log(x)
4452e^x
4453\left[-1, 1\right]
4454x^2
4455\cos(x)
4456\arcsin(x)
4457\left[-1, 1\right]
4458\ln(x)
4459\frac 1 x
4460\sqrt{x}
4461\left[1, 2\right]
4462\log(x)
4463\sqrt{x}
4464\frac 1 x
4465f\left(x\right)=\cos\left(x\right)
4466\text{Im} \left(f\right)
4467(-1, 1)
4468[0, +\infty)
4469[0, 1]
4470[-1, 1]
4471(-\infty, 0]
4472f\left(x\right)=|\cos\left(x\right)|
4473\text{im} \left(f\right)
4474\left[0, 1\right]
4475\left[-1, 0\right]
4476\left[-1, 1\right]
4477\left(-1, 1\right)
4478\left(0, 1\right)
4479F = -kx
4480F = kx
4481F = kx^2
4482F = \frac{k}{x}
4483F = \frac{x}{k}
4484\frac{kx^2}{2}
4485\frac{kx}{2}
4486kx
4487x^2k
4488\frac{x}{k^2}
4489I = VR^2
4490V = \frac{R}{i}
4491V=Ri^2
4492I=VR
4493V=Ri
4494F = \frac{KQq}{r^3}
4495F = \frac{KQq}{r^2}
4496F = \frac{KQq}{r}
4497F = \frac{Kq}{r^3}
4498F = \frac{Qq}{r^3}
4499U = \frac{KQq}{r^3}
4500U = \frac{KQq}{r^2}
4501U = \frac{KQq}{r}
4502U = \frac{KQ}{r^3}
4503U = \frac{Kq}{r^3}
4504P
4505P = R i^2
4506P = \frac{V^2}{R}
4507P = Vi
4508t
4509W = Rit
4510W = Vi^2t
4511W = R\frac{i}{t}
4512W = Ri^2t
4513W = R\frac{i^2}{t}
4514O
4515P
4516\vec{M} = O\vec{P} \times \vec{F}
4517\vec{M} = \vec{F} \times O\vec{P}
4518\vec{M} = FO\vec{P}
4519\vec{M} = OP\vec{F}
4520\vec{M} = OPF
4521n
4522R
4523R_{eq} = \sum_{i} R_i
4524R_{eq} = \prod_{i} R_i
4525R_{eq} = \frac{1} {\sum_{i} R_i}
4526R_{eq} = \sum_{i} \frac{1}{R_i}
4527R_{eq} = \frac{1}{\prod_{i} R_i}
4528n
4529R
4530R_{eq} = \frac{1}{\sum_{i} R_i}
4531R_{eq} = \sum_{i} \frac{1}{R_i}
4532\frac{1}{R_{eq}} = \sum_{i} R_i
4533\frac{1}{R_{eq}} = \frac{1}{\sum_{i} R_i}
4534\frac{1}{R_{eq}} = \sum_{i} \frac{1}{R_i}
4535P
4536O
4537\vec{L} = O\vec{P} \times m\vec{v}
4538\vec{L} = O\vec{P} \times m\vec{a}
4539\vec{L} = OPm\vec{v}
4540\vec{L} = \vec{M} + m\vec{v}
4541\frac{d\vec{l}_0}{dt}
4542\vec{v}_0 \times m\vec{v}_{cm}
4543\vec{M}_e-\vec{v}_0 \times m\vec{v}_{cm}
4544\vec{M}_e
45450
4546\vec{L}_0
4547N
4548\vec{M}_0
4549\vec{L}_0
4550Nk
4551k
45523\cdot 10^{8} \frac{m}{s}
45532.9 \cdot 10^{23} \frac{m}{s}
45546\cdot 10^{2} \frac{m}{s}
455511\cdot 10^{-9} \frac{m}{s}
45561.8\cdot 10^{3} \frac{m}{s}
4557\frac{\lambda}{2m}
4558\frac{k}{m}
4559\frac{2\lambda dx}{dt}
4560\omega x
4561\frac{\lambda}{2 \omega}
4562\frac{\delta}{\omega}
4563\Sigma
4564E
4565\Sigma
4566E
4567\Sigma
4568E
4569\Sigma
4570\Sigma
4571D
4572\Sigma
4573\nabla j + \frac{d\sigma}{dt} = 0
4574\nabla j = \frac{d\sigma}{dt}
4575\nabla j + \frac{d\sigma}{dt} = cost
4576\nabla j - \frac{d\sigma}{dt} = cost
4577\frac{d\sigma}{dt} = \frac{1}{\nabla j}
4578\vec{F}_e = \frac{d\vec{Q}}{dt}
4579\vec{F}_e = m\vec{Q}
4580\vec{F}_e = m\vec{V}
4581\vec{F}_e = m\vec{v}+\frac{d\vec{Q}}{dt}
4582\vec{F}_e = m\vec{v}+\frac{d\vec{L}}{dt}
4583\frac{d\vec{L_0}}{dt} = \vec{M}_0-\vec{v}_o \times m\vec{v}_{cm}
4584\frac{\vec{dL_0}}{dt} = \vec{M_0}
4585\frac{d\vec{L_0}}{dt} = \vec{M_0}+\vec{v_o} \times m\vec{v}_{cm}
4586\frac{\vec{dL_0}}{dt} =0
4587\frac{\vec{dM_0}}{dt} =0
4588I\omega
4589L\omega
4590M\omega
4591\frac{1}{2}I \omega^2
4592\frac{1}{2}L \omega^2
4593\alpha
4594I\omega \alpha
4595I\alpha
4596M\alpha
4597IM
4598I\omega
4599I\omega
4600M\alpha
4601I\alpha
4602MI
4603LI
4604\frac{1}{\sqrt{2}}
4605\sqrt{2}
4606\frac{1}{\sqrt{2}}
4607\sqrt{2}
4608\omega^2=\frac{g}{l}
4609\omega
4610\omega
4611\omega ^2
4612\omega ^2
4613\sqrt{\omega}
4614\alpha
4615\alpha
4616\alpha
4617\alpha
4618\alpha
4619\omega
4620\sqrt{\frac{g}{L}}
4621\sqrt{\frac{L}{g}}
4622\frac{g}{L}
4623\frac{L}{g}
4624\alpha
4625\alpha
4626\alpha
4627\alpha
4628\alpha
4629\rho
4630V
4631g
4632F=\frac{\rho g}{V}
4633F=\frac{gV}{\rho}
4634F=\rho gV
4635F=\frac{V}{\rho g}
4636F=\frac{g}{\rho V}
4637273 \ K
46380
46390
4640273 \ K
46410
4642\frac{g}{3}
4643\frac{g}{9}
46443g
46459g
46466g
464745^\circ
4648M
4649E
4650E
4651D
4652B
4653\Sigma
4654\int{B \cdot \vec{u}_n d\Sigma}
4655\int {\frac{B \cdot \vec{u}_n} {d{\Sigma}}}
4656\int {B d\Sigma}
4657\int {\vec{u}_n d\Sigma}
4658\int {B \times \vec{u}_n d\Sigma}
4659q
4660m
4661v
4662B
4663q
4664m
4665v
4666B
4667F = q v B
4668F = q v B \sin \theta
4669F = \frac{q v B}{\sin \theta}
4670F = \frac{q v}{B} \sin \theta
4671F = \frac{q}{v} B \sin \theta
4672B
4673E
4674B
4675d\vec{F}=id\vec{s} \times \vec{B}
4676d\vec{F}=d\vec{s} \times \vec{B}
4677d\vec{F}=jd\vec{s} \times \vec{B}
4678d\vec{F}=id\vec{s} \vec{B}
4679d\vec{F}=i\frac{d\vec{s}} {\vec{B}}
4680l
4681B
4682F = l B \sin \theta
4683F = l B \cos \theta
4684F = i l B \sin \theta
4685F = i l B \cos \theta
4686F = i l B
4687F
4688S
4689F
4690S
4691F
4692S
4693F
4694S
4695F
4696S
469745^\circ
4698F
4699S
4700135^\circ
47010
47021
47031
4704C
4705i
4706\sigma
4707C
4708W=i \Delta \phi
4709W=-i \Delta \phi
4710W=\frac{i} {\Delta \phi}
4711W=-\frac{i} {\Delta \phi}
4712W=i^2 \Delta \phi
4713\frac{Kg}{A s^2}
4714\frac{Kg}{A s}
4715 KgAs^2
4716KgAs
4717\frac{KgA}{s^2}
4718\frac{kg}{A s^2}
4719\vec{B}=\frac{\mu_0i}{4\pi} \frac{\int(\vec{ds} \times \vec{u_r})}{r^2}
4720\vec{B}=\frac{\int(\vec{ds} \times \vec{u_r})}{r^2}
4721\vec{B}=\frac{\mu_0i}{4\pi} \int(\vec{ds} \times \vec{u_r})r^2
4722\vec{B}= \frac{\int(\vec{ds} \times \vec{u_r})}{r^2}
4723\vec{B}=\frac{\mu_0i}{4\pi} \frac{\int(\vec{ds} \times \vec{u_r})}{r}
4724\vec{B} =\frac{\mu_0}{4\pi}\frac{q\vec{v} \times \vec{u_r}}{r^2}
4725B
4726\vec{B} =\frac{\mu_0}{4\pi}\frac{q\vec{v} \times \vec{u_r}}{r^2}
4727\vec{B} =\frac{\mu_0}{4\pi}q\vec{v} \times \vec{u_r}r^2
4728\vec{B} =\frac{q\vec{v} \times \vec{u_r}}{r^2}
4729\vec{B}=q\vec{v} \times \vec{u_r}
4730\vec{B}=\frac{\mu_0}{4\pi} \frac{q \vec{v} \times \vec{u_r}}{r}
4731\nabla \times B=0
4732\nabla B=0
4733\nabla \times B=\mu_0 j
4734\nabla B=0
4735\nabla \times B=0
4736\nabla B=\mu_0 j
4737\nabla \times B=\frac{1}{\mu_0}j
4738\nabla B=0
4739\nabla \times B=0
4740\nabla B=\frac{1}{\mu_0}j
4741H
4742\nabla \times H = 0
4743\nabla \times H = \mu_0 J
4744\nabla \times H = J
4745\nabla \times H = \mu_0
4746\nabla \times H = \frac{1}{\mu_0}
4747H
4748H = \frac{B}{\mu_0} - M
4749H = B\mu_0 - M
4750H = \frac{B}{\mu_0} + M
4751H = B\mu_0 + M
4752H = B-M\mu_0
4753H
4754M
4755m
4756\theta
475710 \ kg
475898\ N
475910\ N
476045\ N
4761450\ N
4762890\ N
476336 \ \frac{km}{h}
4764\frac{m}{s}
47650,36\ \frac{m}{s}
476636000\ \frac{m}{s}
476736\ \frac{m}{s}
476810 \ \frac{m}{s}
4769100 \ \frac{m}{s}
4770r
4771v
4772mvr^2
4773\frac{mv^2}{r}
4774\frac{1}{2} \frac{mv^2}{r}
4775\frac{vr^2}{m}
4776\frac{vm}{2}
4777100 \ \frac{km}{h}
4778O
4779O
4780T
47811
478225 \ \frac{J}{K mole}
4783200 \ \frac{J}{K mole}
4784151.6 \ \frac{J}{K mole}
478567.6 \ \frac{J}{K mole}
4786273.15 \ \frac{J}{K mole}
4787T
47881
47891 \ cal = 4186.8 \ J
47904 \ cal = 1.2 \ J
47911 \ cal = -4186 \ J
47921 \ cal = 0,412 \ J
47934 \ cal = 1486.6 \ J
4794dW=pdV
4795\gamma
47961 \ m
47972 \ cm^2
47980,80 \ m
47990,1 \ m^2
48001,40 \ m
48011 \ cm^2
48022 \ m
48031 \ cm^2
48040,1 \ m
48050,1 \ cm^2
4806\Delta G < 0
4807\Delta H > 0
4808\Delta S = 0
4809\Delta G > 0
4810\Delta S < 0
481110 \ m
48120,1 \ atm
48131 \ atm
48142 \ atm
48155 \ atm
481610 \ atm
4817620-750 \ nm
48181 \ m
48191,5 \ m
482090 \ m
482140 \ m
482260 \ m
482380 \ m
4824100 \ m
4825135 \ m
48265 \ N
482710 \ N
48285 \ N
482925 \ N
483050 \ N
4831T^2
4832a^3
4833T^2
4834a^3
4835T^2
4836a^3
4837\vec{q}_{fin} - \vec{q}_{in}
4838\vec{L}_{fin} - \vec{L}_{in}
4839\vec{q}_{in} - \vec{q}_{fin}
4840\vec{L}_{in} - \vec{L}_{fin}
4841\vec{q}_{in} - \vec{q}_{fin} = \int_{t_{in}}^{t_{fin}} \vec{F} \,dt
4842\vec{q}_{fin} - \vec{q}_{in} = \int_{t_{in}}^{t_{fin}} \vec{F} \,dt
4843\vec{L}_{fin} - \vec{L}_{in} = \int_{t_{fin}}^{t_{in}} \vec{F} \,dt
4844\vec{L}_{fin} - \vec{L}_{in} = \int_{t_{in}}^{t_{fin}} \vec{L} \,dt
4845\vec{q}_{fin} - \vec{q}_{in} = \vec{L}_{fin} - \vec{L}_{in}
4846\vec{q}_{fin} - \vec{q}_{in} = \int_{t_{in}}^{t_{fin}} \vec{F} \,dt
4847\vec{q}_{in} - \vec{q}_{fin} = \int_{t_{in}}^{t_{fin}} \vec{M} \,dt
4848\vec{L}_{in} - \vec{L}_{fin} = \int_{t_{in}}^{t_{fin}} \vec{F} \,dt
4849\vec{L}_{fin} - \vec{L}_{in} = \int_{t_{in}}^{t_{fin}} \vec{M} \,dt
4850\vec{L}_{fin} - \vec{L}_{in} = 0
4851\vec{q}_{fin} - \vec{q}_{in} = \int_{t_{in}}^{t_{fin}} \vec{F} \,dt
4852\vec{k}_{fin} - \vec{k}_{in} = \int_{t_{in}}^{t_{fin}} \vec{F} \,d\vec{r}
4853\vec{k}_{in} - \vec{k}_{fin} = \int_{x_{in}}^{x_{fin}} \vec{F} \,dt
4854\vec{k}_{fin} - \vec{k}_{in} = \int_{x_{fin}}^{x_{in}} \vec{F} \,dt
4855\vec{w} \times (\vec{a} \times \vec{r})
4856\vec{w} \times (\vec{v} \times \vec{r})
4857\vec{M} \times (\vec{w} \times \vec{r})
4858\vec{w} \times (\vec{w} \times \vec{r})
4859\vec{L} \times (\vec{w} \times \vec{r})
4860\vec{w} \times \vec{w} \times \vec{v}
48612\vec{w} \times \vec{v}
4862\vec{w} \times \vec{v}
4863-\vec{w} \times (\vec{w} \times \vec{r})
4864-m\vec{w} \times (\vec{w} \times \vec{r})
4865-m \times (\vec{w} \times \vec{r})
4866-m\vec{r} \times (\vec{w} \times \vec{r})
4867-m\vec{w} \times (\vec{w} \times \vec{v})
4868-m\vec{\omega} \times \vec v
4869-2m\vec{\omega} \times \vec r
4870-2m\vec{\omega} \times \vec v
4871-4m\vec{\omega} \times \vec v
4872-2m\vec{\omega}r \times \vec v
4873\pi GM
4874GM
48750
4876\pi KG
4877QG\pi
48780
4879KG\pi
4880UG\pi
4881MK
4882\vec Q = M\vec{a_{cm}}
4883\vec Q = \vec{L} \times \vec{a_{cm}}
4884\vec Q = MG
4885\vec Q = \vec{v} \times \vec{a_{cm}}
4886\vec Q = M\vec{v_{cm}}
4887Q \vec{a}_{cm}
4888M \vec{v}_{cm}
4889M \vec{a}_{cm}
4890M \vec{Q}
48910
4892\vec{M}_o=\vec{R}_g \times M\vec{V}_g + \vec{l}_g
4893\vec{L}_o=\vec{R}_g \times M\vec{V}_g + \vec{l}_g
4894\vec{Q}_o=\vec{R}_g \times M\vec{V}_g + \vec{l}_g
4895\vec{L}_o=\vec{R}_g \times M\vec{A}_g + \vec{l}_g
4896\vec{L}_o=\vec{M}_o \times M\vec{V}_g + \vec{l}_g
4897K=\frac{1}{2}M{a_g}^2 + k_g
4898K=\frac{3}{2}M{V_g}^2 + k_g
4899K=M{V_g}^2 + k_g
4900K=\frac{1}{2}M{v_g}^2 + k_g
4901K=0
4902\alpha
4903L_\alpha \omega_\alpha
4904I_\alpha \omega_\alpha
4905I_\alpha M_\alpha
4906M_\alpha \omega_\alpha
4907L_\alpha M_\alpha
4908L
4909L^2
4910\frac{1}{12}ML^2
4911\frac{1}{12}ML^3
4912ML^2
4913\frac{1}{2}w
4914\frac{1}{2}\vec{w} \times \vec{l_g}
4915\vec{w}\vec{l_g}
4916\frac{1}{2}\vec{w} \vec{l_g}
4917\frac{3}{2}\vec{w} \times \vec{l_g}
4918L
49190
4920\frac{1}{12}ML^2
4921\frac{1}{2}WLg
4922ML^2
4923ML^3
4924R
49250
4926\frac{1}{2}MR^2
4927MR^2
4928\frac{M}{R}
4929\frac{M}{2R}
4930R
4931\frac{1}{2}MR^2
4932\frac{1}{2}M^2
4933MR^2
4934\frac{1}{2}R^2
4935R^2
4936R
4937\frac{1}{2}R^2
49380
4939MR^2
4940\frac{1}{2}MR^2
4941R
4942\frac{1}{2}MR^2
4943\frac{1}{3}MR^2
4944\frac{1}{4}MR^2
4945MR^2
4946\frac{1}{4}R^2
4947I
4948d
4949I+{d^2}
4950{I^2}+d
4951{I^2}+Md
4952{I+Md}
4953I+M{d^2}
4954\varepsilon
4955\varepsilon>1
4956\varepsilon=1
49570<\varepsilon<1
4958\varepsilon=0
4959\varepsilon
4960\varepsilon>1
4961\varepsilon=1
49620<\varepsilon<1
4963\varepsilon=0
4964\varepsilon
4965\varepsilon>1
4966\varepsilon=1
49670<\varepsilon<1
4968\varepsilon=0
4969\varepsilon
4970\varepsilon>1
4971\varepsilon=1
49720<\varepsilon<1
4973\varepsilon=0
49741\ km/h
4975100\ km/h
4976km
4977200\ km/h
4978150\ km/h
497990
498090
498190
4982y
4983x
4984x
4985h
4986h
4987h
4988h
4989q
4990\sigma
4991R
4992E
4993E
4994E
4995E
4996E
4997q
4998\sigma
4999R
5000E
5001E
5002E
5003E
5004E
5005E
50063\ \Omega
50072\ \Omega
50085\ \Omega
500910\ \Omega
5010325\ \Omega
5011532\ \Omega
50125003.002\ \Omega
50132003.005\ \Omega
5014d\Sigma
5015i
5016dm = id\Sigma \mu_n
5017i
5018h
5019\frac{D^2 x(t)}{dt^2} + \omega^2 x(t) = 0
5020\frac{D^2 x(t)}{dt^2} - \omega^2 x(t) = 0
5021\frac{D^2 x(t)}{dt^2} + \omega x(t) = 0
5022\frac{D^2 x(t)}{dt^2} - \omega x(t) = 0
5023\frac{D^2 x(t)}{dt^2}{\omega^2 x(t)} = 0
5024f\colon\ [0,4]\to \mathbb{R}
5025\lim_{x \to 2}(f(x))
5026f(2)=0
5027f^{'}(x)
5028x=2
5029f(x)
5030x=2
5031f^{'}(x)
5032x
5033[0,4]
50340
50350
5036R=0
5037M=0
5038T=0
5039\omega =0
5040v=0
5041v=0
5042R=0
5043v=0
50440
50451
5046\infty
50472
50483
50494
50503
50514
50525
5053M
5054\sqrt{\frac{2M}{R}}
5055\frac{2GM}{R}
5056\sqrt{\frac{2GM}{R}}
5057\sqrt{\frac{2G}{R}}
5058\sqrt{\frac{GM}{R}}
5059\frac{N}{{Kg}^2}
5060\frac{N{m^2}}{{Kg}^2}
5061\frac{N{m^3}}{{Kg}^2}
5062\frac{m^2}{{Kg}^2}
5063Nm^2
5064M
5065R
5066-\frac{GM}{R^2}
50670
5068-\frac{M}{R^2}
5069-\frac{G}{R^2}
5070-\frac{GM}{R^3}
5071M
5072R
5073r
5074-\frac{G}{r^2}
5075-\frac{GM}{r^2}
50760
5077-\frac{M}{r^2}
5078-\frac{GM}{r}
5079M
5080\pi GM
50814\pi GM
5082-\pi GM
5083-4\pi GM
5084-4\pi M
5085Q
50860
50874\pi Q
50884\pi K
5089\pi KQ
50904\pi KQ
5091\mu
5092\frac{2\mu}{r}
5093\frac{k\mu}{r}
5094\frac{2k}{r}
5095\frac{2k\mu}{r}
50962k\mu
5097\sigma
5098\frac{\sigma}{2\epsilon_0}
5099\frac{\sigma}{\epsilon_0}
5100\sigma 2\epsilon_0
5101\left(\frac{\sigma}{2\epsilon_0} \right)^2
5102\frac{\sigma^2}{2\epsilon_0}
5103\sigma
5104\epsilon_0
5105\frac{\sigma}{2\epsilon_0}
5106\frac{\sigma}{\epsilon_0}
5107-\sigma 2\epsilon_0
5108\sigma 2\epsilon_0
5109\sigma +2\epsilon_0
5110\sigma
5111\epsilon_0
5112d
5113-\sigma d\epsilon_0
5114-\frac{\sigma d}{\epsilon_0}
5115\frac{\sigma d}{\epsilon_0}
5116-\frac{\sigma}{\epsilon_0}
5117\rho
5118p+\rho gz = cost.
5119p+gz = cost.
5120p\rho z = cost.
5121p+gz = cost.
5122p+ \rho z = cost.
51231\ bar
5124780\ mmHg
51251,071\ atm
5126760\ mmHg
5127760\ Pa
5128\frac{1}{2} \rho {v^2}+\rho g+p=cost.
5129\frac{1}{2} \rho {v^2}+\rho z+p=cost.
5130\frac{1}{2}\rho v+\rho gz+p=cost.
5131\frac{1}{2}\rho {v^2}+ \rho gz+p=cost.
5132 \rho{v^2}+\rho gz+p=cost.
5133p=nRT
5134pV=nR
5135pV=nRT
5136pV=nT
5137pV=RT
51380\ K
5139+273.15^\circ C
51400^\circ C
5141-273.15^\circ C
5142273,15\ Pa
5143-273,15\ Pa
5144{6,022}\cdot 10^{23}
5145{5,022}\cdot 10^{23}
5146{6,022}\cdot 10^{23}
5147{6,022}\cdot 10^{-23}
5148{K_b}T
5149\frac{3}{2} {T}
5150\frac{3}{2} {K_b}
5151\frac{3}{2} {K_b}{T}
5152\frac{3}{2} \frac{K_b}{T}
5153\frac{f}{2} \frac{K_b}{T}
5154\frac{f}{2} {K_b}T
5155\frac{3}{2} {K_b}T
5156\frac{f}{2} {K_b}
5157\frac{3}{2} {K_b}{T^2}
5158pV=K_bT
5159pV=NK_bT
5160pV=NK_b
5161pV=nRT
5162pV=NT
5163Q>0
5164L>0
5165dU=Q+L
5166dU=Q-L
5167dU=QL
5168dU=\frac{Q}{L}
5169dU=Q^L
5170U
517190
517290
517390
51740
517590
517690
517790
51780
5179m
5180r
51811
51820
51832\pi rm
51842\pi rwm
51852 \pi{r^2}{w^2}
51862\pi{r^2}{w^2}m
51870
51880
51890
51900
51910
5192T
51932l
51944l
5195\frac{1}{2}l
5196\frac{1}{4}l
519710 \ kg
519810 \ kg
519910\ kg
520010 \ kg
52010 \ kg
5202v
5203\frac{N}{s}
5204\frac{Nm}{s}
5205\frac{Nm}{s^2}
5206\frac{Kgm}{s}
5207J
52081 kg
520928 kg \frac m s
52100 \frac m/s
521128 \frac m/s
52127.8 \frac m/s
52133.6 \frac m/s
5214T_1=800\ K
5215T_2=200\ K
52168\ kJ
52171\ kJ
52182\ kJ
52193\ kJ
52206\ kJ
52218\ kJ
52220
52230
52240
5225180
5226270
5227T_A
5228T_B
5229T_A
5230T_A=T_B
5231T_A>T_B
5232dT
5233 \frac f 2 K_b \ dT
5234 \frac f 2 \ dT
5235 \frac f 2 R \ dT
5236 \frac 1 2 K_b \ dT
5237 \frac 3 2 K_b \ dT
5238dT
5239\frac f 2\ dT
5240\frac 1 2 K_b \ dT
5241\frac 3 2 K_b \ dT
5242\frac 1 2 R\ dT
5243\frac f 2 K_b \ dT
5244c_v\ dT
5245nc_p\ dT
5246nc_v\ dT
5247nc_v
5248nc_p
5249nc_v\ d
5250c_v\ dT
5251nc_p
5252nc_v\ dT
5253nc_p\ dT
5254 c_p=\frac {c_v}{R}
5255 c_p=c_v R
5256 c_p=R
5257 c_p=c_v-R
5258 c_p=c_v+R
5259c_p
5260\frac 3 2 R
5261\frac 5 2 R
5262\frac 7 2 R
5263\frac 9 2 R
5264\frac 11 2 R
5265c_v
5266\frac 1 2 R
5267\frac 3 2 R
5268\frac 5 2 R
5269\frac 7 2 R
5270\frac 9 2 R
5271\frac {L_{syst}}{Q_{ced}}
5272\frac {L_{syst}}{Q_{ass}}
5273\frac {L_{syst}}{Q_{tot}}
5274\frac {L_{amb}}{Q_{ced}}
5275\frac {L_{amb}}{Q_{ass}}
5276nc_v\ dT
5277c_v dT
5278nc_p
5279nc_v
5280nc_p\ dT
5281Q
5282nR\ln\left(\frac{T_f}{T_i}\right)
5283nc_v\ dT
5284L
5285\frac f 2 K_b\ dT
5286nc_p
5287nc_v
5288nRT
52890
5290nc_v\ dT
5291nc_p\ dT
52920
5293nRT\ln\left(\frac{V_f}{V_i}\right)
5294\frac 1 3 rm^2
5295\frac 3 8 mr^3
5296\frac 1 2 m^2 r^2
5297\frac 2 5 mr^2
5298\frac 1 3 mr^2
5299N
5300Kg \frac m s
5301\frac N s
5302N \frac m s
5303N
5304Kg\frac m s
5305\frac N s
5306N \frac m s
5307N\frac m s
5308\frac N s
5309J
5310\frac J s
53111
53122
53133
53144
53155
5316G
53178
53184
53196
53202
53211
532210^5\ Pa
532310^4\ Pa
532410^5\ mmHg
532510^5\ atm
53262\ kNm^2
532710^3\ Pa
53281\ MNm^2
532910^7\ Pa
533010^5\ Pa
53310
53320^{\circ}
533345^{\circ}
533490^{\circ}
5335145^{\circ}
5336270^{\circ}
5337N\cdot m\cdot s
5338N\cdot \frac m s
5339kg\cdot m\cdot s
5340kg\cdot \frac m s
5341N\cdot m
5342N\cdot m\cdot s
5343N\cdot \frac m s
5344N\cdot m
5345kg\cdot m\cdot s
5346kg\cdot \frac m s
5347J
5348kg\cdot m
5349kg\cdot \frac m s
5350kg\cdot m\cdot s
5351N\cdot m\cdot s
5352N\cdot m
5353\frac{N}{m}
5354N
5355N\cdot m^2
53560
53570
53581
53591
53601
53610
53621
53631
53641
53651
5366\frac R L
5367R\cdot L
5368\frac L R
5369R+L
5370\frac N C
5371\frac V C
5372\frac A V
5373\frac C V
5374\frac C m
5375\frac{J}{Kg\cdot K}
5376\frac{J}{K}
5377J\cdot K
5378\frac{J}{mol\cdot K}
5379\frac{J}{K^2}
53801
53811
53820
53831
53840
538590
53860
5387180
5388L
5389i
5390B
5391F=\frac {iB} L
5392F=\frac {BL} i
5393F=\frac {Li} B
5394F=\frac B {iL}
5395F=iBL
5396\frac {cal\cdot g} K
5397\frac K {cal\cdot g}
5398\frac g {cal\cdot K}
5399\frac cal {g\cdot K}
5400\frac {cal\cdot K} g
5401\frac {g} {cal\cdot K}
5402\frac {cal} {g}
5403\frac {g} {cal}
5404\frac {cal\cdot g} {K}
5405\frac {cal} {g\cdot K}
54061 \ ^{\circ} C
54071\ g
540814,5\ ^{\circ} C
54091,5 \ J
541010 \ erg
54115 \ kcal
54122,5 \ kWh
54131 \ cal
54140
541510\ \Omega
541620\ V
54175 \ A
541810 \ A
54192 \ A
542020 \ A
5421200 \ A
5422J
5423K
5424\frac{K}{J}
5425\frac{K}{mol}
5426\frac{J}{K}
54273
5428\frac 1 9
54296
54309
5431 \frac 1 3
54325F
543330F
543430
54355
543625
54376
543843252
5439100\ ^{\circ} C
5440-273\ ^{\circ} C
54410\ ^{\circ} C
5442-40\ ^{\circ} C
544357\ ^{\circ} C
54440
54451
54460
54471
5448P=IV
5449P=\frac I V
5450P=\frac V I
5451P=\frac 1 {IV}
5452x
5453k
5454F=\frac k x
5455F=-kx
5456F=\frac x k
5457F=-\frac x k
5458F=kx
54598
54604
54612\ kg
546220\ m
5463 10\ \frac m s
5464 20\ \frac m s
5465 30\ \frac m s
5466 60\ \frac m s
5467 80\ \frac m s
54682\ kg
546920\ m
54705\ J
5471100\ J
5472200\ J
5473400\ J
5474800\ J
5475100\ \frac N m
54762\ m
5477200\ J
547825\ J
547950\ J
5480400\ J
5481100\ J
5482\frac 1 4
5483200\ \frac N m
548450\ N
54850,05\ m
54860,10\ m
54870,15\ m
54880,20\ m
54890,25\ m
5490 |a+b| \leq |a|+|b|
5491 |a+b| \geq |a|-|b|
5492 |a+b| \leq |b|-|a|
5493 |a| \geq a
5494 |a+b+c| \leq |a|+|b+c|
5495\mathbb{N} \subset \mathbb{R} \subset \mathbb{Q}
5496\mathbb{Q} \subset \mathbb{R} \subset \mathbb{N}
5497 \mathbb{R} \subset \mathbb{Q} \subset \mathbb{N}
5498 \mathbb{R} \subset \mathbb{N} \subset \mathbb{Q}
5499\mathbb{N} \subset \mathbb{Q} \subset \mathbb{R}
5500W
5501\frac{J}{s}
5502CV
5503eV
5504\frac{cal}{s}
5505\frac 1 2
5506\frac 1 2
5507\frac 1 2
5508\frac 1 2
55090,01 \ m
551050 \ \frac V m
55110,5\ V
55125\ V
551350\ V
5514100\ V
55150,05\ V
55161 F
55172 F
55183 F
55191,5 F
5520\frac 2 3 F
55212,5 F
55221 F
5523U
5524x
55252U
5526\frac U 2
55274U
5528\frac U 4
5529\left[ \sqrt{2} , \pi \right)
5530V\cdot R
5531\frac V L
5532\frac L R
5533\frac V R
5534R\cdot L
5535 \frac R C
5536\frac C V
5537\frac V {RC}
5538\frac C R
5539 C\cdot V
5540\frac V R
5541 R \cdot C
5542\frac C V
5543 \frac R C
5544 C\cdot V
554510
5546-3
5547-6
5548-9
5549-12
5550-15
55510^{\circ}
555245^{\circ}
555390^{\circ}
5554135^{\circ}
5555180^{\circ}
5556\frac L T
5557\frac 1 T
5558T
5559\frac 1 L
5560\frac T L
5561X
5562A
5563I\left(x\right)
5564x
5565A
5566x
5567A
5568x
5569A
5570x
5571A
5572P\cdot T
5573\frac P T
5574P\cdot V
5575\frac V T
5576\frac P V
5577V\Delta P
55780
5579V\Delta T
5580P\Delta T
5581P\Delta V
5582R\Delta T
5583R\Delta V
5584T\Delta P
5585P\Delta T
5586Cv
5587Cp
5588R
5589R=\frac Cv Cp
5590R=Cp-Cv
5591R=Cp\cdot Cv
5592R=Cv-Cp
5593R=Cp+Cv
5594 \frac {Kg} {m^3}
5595\frac {Kg} {m^2}
5596\frac {Kg} m
5597 N\cdot m^2
5598 \frac Kg m
5599 \frac m N
5600kg\cdot m^2
5601N
56022 \ kg
56035 \ m
560450\ kg\cdot m^2
560525\ kg\cdot m^2
5606\frac {100} {3} \ kg\cdot m^2
560720\ kg\cdot m^2
5608\frac {10} {3} \ kg\cdot m^2
56095\ \Omega
5610200\ V
561120 A
56121000 A
5613100 A
561440 A
5615400 A
5616V
5617N
5618Pa
5619C
5620A
5621di risorse e posizioni?
5622sanzione??
5623reali saranno le conseguenze"?
5624\frac{C}{N\cdot m}
5625\frac{N}{m\cdot C}
5626\frac{C}{m^2}
5627\frac{F}{m}
5628A
5629V
5630\frac{J}{C}
5631\frac{N\cdot m}{C}
5632ad una situazione?
563310^13
563410^9
563510^15
563610^12
5637G_1
5638G_2
5639G_1
5640G_2
5641G_1
5642G_2
5643G_1
5644G_2
5645G_1
5646G_2
5647H^+
5648OH^–
5649H^–
5650OH^+
5651OH^–
5652n^2(n
5653H^+
5654H^+
5655OH^–
5656OH^–
5657H_2
5658cm^3
5659dm^3
5660H^+
5661OH^–
5662H^+
5663OH^–
5664H_2S
5665H_2SO_4
5666H_2SO_3
5667Na_2SO_4
5668K_2S
566910^–27
567010^–27
567110^–17
567210^–35
567310^–27
5674Cl_2O_3
5675NH_3
5676Al_2O_3
5677Na_2O
5678Ca_3(PO_4)_2
5679CaPO_4
5680Ca_3(PO_4)_3
5681Ca_3(HPO_4)_2
5682Ca_3P_2
5683Mg(OH)_2
5684MgH_2
5685O_2
5686H_2O_2
5687OH^–
5688H_2MgO
56891/2O_2
56902NaNO_3
56912NaNO_2
5692O_2
56933NaNO_2
5694O_2
56952NaNO_3
56962NaNO_2
56973/2O_2
5698NaNO_3
5699NaNO_2
5700O_2
57012NaNO_3
57022NaNO_2
57033O_2
5704SO_3
5705SO_2
5706SO_4
5707H_2S
5708H_2SO_4
5709KH(IO_3)_2
5710KHIO_3
5711KHI_2
5712KH(IO)_2
5713H_3PO_4
5714H_2PO_3
5715H_2PO_4
5716H_3PO_3
5717H_4PO_4
5718Ba(HSO_4)_2
5719Ba(HSO_3)_2
5720BaSO_4
5721Ba(HS)_2
5722BaH_2SO_4
5723HCO_3^–
5724(CO_3^2–)_2
5725H_2CO_3^–
5726CO_2^2–
5727Na_2S
5728Na_2SO_3
5729NaSO_4
5730Na_2SO_4
5731CO_3^2–
5732CO_2^–
5733HCO_3^–
5734CO_3^2+
5735HCO_2^–
5736HClO_4
5737HClO_3
5738HClO_2
5739Nb_2O_5
5740NbO_3
5741Nb_2O_3
5742Nb_2O_4
5743Nb_4O_10
5744NaH_2PO_4
5745H_5PO_3
5746KCl_2
5747H_3CO_3
5748CaH_2SO_3
5749Ca_3(PO_4)_2
5750Ca_3(PO_3)_2
5751CaHPO_3
5752CaHPO_4
5753Ca_2(PO_4)_3
5754MgO_2
5755Mg(OH)_2
5756Mg_2O_3
5757ClO_4^–
5758Cl^–
5759ClO^–
5760ClO_2
5761CO_2
5762C_2O
5763C_2O_2
5764C_2SO_2
5765H_2S_2O_3
5766H_2SO_4
5767H_2SO_3
5768H_2S
5769SO_2
5770S_2O_3
5771SO_3
5772H_2SO_4
5773Al(OH)_3
5774Al_2O_3
5775Al_3(OH)_3
5776Al_2O
5777^oC)
5778^oC)
5779CO_3^2–
5780CO_2
5781CO^2–
5782C^+
5783Fe(OH)_3
5784Fe(OH)_2
5785Fe_2O_3
5786FeH_2
5787NaHCO_3
5788Na_2CO_3
5789CH_3COONa
5790CH_3COONH_4
5791K_2SO_4
5792H_2SO_5
5793H_2SO_4
5794H_2SO_3
5795H_2S
5796H_2S_2O_7
5797sp^2
5798CH_3-CH_2-CH_3
5799CH_4
5800CH_3-CH_2-CH_2-CH_2-CH_3
5801CH_3-CH_2-CH_2-CH_3
5802sp^3
5803sp^3
5804sp^2
5805sp^2
5806sp^2
5807sp^3
5808sp^3
5809sp^2
5810CO_2
5811H_2O
5812H_2O
5813CH_2Cl_2
5814CH_2
5815CCl_4
5816CHCl_3
5817CH_3-CH_2-COOH
5818CH_3-CH_2-CO-O-CO-CH_2-CH_3
5819CH_3-CH_2-CHO
5820CH_3-CO-CH_3
5821CH_3Cl
5822CH_3CH_2OH
5823C_6H_5Cl
5824CH_3COCl
5825CH_3OCH_3
5826C_6H_6
5827C_6H_14
5828C_6H_12
5829C_6H_10
5830C_6H_8
5831-NO_2
5832-NH_2
5833CH_4
5834C_6H_6
5835C_2H_6
5836C_2H_4
5837C_2H_5OH
5838CH_3OH
5839CH_3OCH_3
5840CH_3NH_2
5841NO_2
5842NH_3
5843CH_3CONH_2
5844CH_3COOCH_3
5845CH_3NO_2
5846CH_3NHCH_3
5847CH_3NH_2
5848–NH_2
5849RCONH_2
5850CO_2
5851H_2O
5852CO_2
5853CO_2
5854O_2
5855H_2O
5856O_2
5857CO_2
5858H_2
5859dell'O_2
5860(l_0)
5861l_0
5862l_0
5863dell'O_2
5864dell'HO_2
5865CO_2
5866dell'O_2
5867H_2O
5868CO_2
5869CO_2
5870O_2
5871CO_2
5872H_2O
5873g/cm^3
5874g/cm^3
5875g/cm^3
5876mg/cm^3
5877mg/cm^3
5878cm^3
587910^–4
5880cm^3
588110^3
5882cm^3
5883cm^3
5884cm^3
5885w_C
5886w_T
5887w_C
5888w_T
5889w_C
5890w_T
5891w_C
58921/w_T
5893w_C
5894w_T
5895kg/m^3
5896g/m^3
5897g/m^3
5898g/m^3
5899kg/m^3
5900m/s^2,
5901m/s^2,
5902m/s^2,
5903m/s^2,
5904m/s^2
5905m/s^2
5906m/s^2
5907m/s^2
5908m/s^2
5909m/s^2
5910m/s^2
59113mv^2
5912mv^2
59132mv^2
5914mv^2
59155mv^2
5916R_1
5917R_2
5918P_C > P_L
5919P_C < P_L
5920P_C = P_L
59219,81 \cdot P_C = P_L
5922V \cdot P_C = P_L
5923m^3
5924m^3
5925P_0
5926P_0
5927P_0/2
5928m/s^2
5929m/s^2
5930m/s^2
5931m/s^2
5932m/s^2
5933m/s^2
5934m/s^2
5935m/s^2
5936m/s^2
5937m/s^2
5938d_fluido
5939N/m^3
5940N/m^3
5941N/m^2
5942s^–1
5943s^–1
5944v = 4ms^{-1}
5945a = 2ms^{-2}
5946V_0
5947V_0/2
5948V_0/4
59492V_0
59504V_0
595110^2
5952µ_o·µ
5953µ_r·µ
5954m/s^2
5955m/s^2
5956m/s^2
5957m/s^2
5958m/s^2
5959m/s^2
5960m/s^2
5961m/s^2
5962m/s^2
5963m/s^2
5964m/s^2
5965m/s^2
5966m/s^2
5967m/s^2
5968m/s^2
5969m^2
5970m^2
5971m^2
5972m^2
5973m^2
5974km^2
5975km^2
5976km^2
5977km^2
5978km^2
5979N_2
5980O_3
5981(m^3/s)
5982(m^3/anno)
5983sen^2(x)
5984cos^2(x)
5985cos^2(x)
5986sen^2(x)
5987sen^2(x)
5988cos^2(x)
5989cos^2
5990sen^2
5991cosα)^2α
5992cos^2αα
5993sen^2αα
5994cos^2αα
5995sen^2αα
5996\frac{1}{\sqrt{2}}
5997cos^2(x)
5998sen^2(x)
5999cos^2(x))
6000cos^2(x)
6001sen^2(x)
6002sen^2(x)
6003cos^2(x)
6004sen^2(x))
60052cos^2(x)
6006cot^2(x)
60071/cos^2(x)
6008cos^2(x)
6009sen^2(x)
6010cos^2(x))
60112cos^3(α)α
60123cos^2(α)α
6013–2cos^3(α)α
60143cos^2(α)α
6015–cos^2(α)α
60162cos^3(α)α
6017cos^2(α)α
6018cos^2(α)α
60194sen(α)cos^2(α/2)αα
60204sen(α)cos^2(α)αα
60212sen^3(α)α
6022–4sen^3(α)α
6023–2sen^2(α)α